diff --git a/Copy_of_LS_DS_133_High_Dimensional_Data_Assignment.ipynb b/Copy_of_LS_DS_133_High_Dimensional_Data_Assignment.ipynb new file mode 100644 index 00000000..c8b3e3da --- /dev/null +++ b/Copy_of_LS_DS_133_High_Dimensional_Data_Assignment.ipynb @@ -0,0 +1,132201 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "Copy of LS_DS_133_High_Dimensional_Data_Assignment.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7wMWCkE1RZpM", + "colab_type": "text" + }, + "source": [ + "# Vertical Line Test" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "W0-g7aprRv2j", + "colab_type": "text" + }, + "source": [ + "## 1.1 Create two graphs, one that passes the vertical line test and one that does not." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "fIJhCtF6RW_U", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import pandas as pd \n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "plt.rcParams.update({'font.size': 14})" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "NPbV1f_4yqZt", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "outputId": "15573b2d-4f28-4499-913a-cf936ec51e14" + }, + "source": [ + "x = np.arange(-11,11)\n", + "y = x*2\n", + "plt.plot(x,y)\n", + "plt.axvline(x=0, color='r');" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Ky1TDoL1zGxS", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "outputId": "c9d95297-39dc-4e74-9f66-da0018f6a4a9" + }, + "source": [ + "y = np.arange(-3,3)\n", + "x = np.cos(y) \n", + "plt.plot(x,y)\n", + "plt.axvline(x=0, color='r');" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ckeTKqMgRy7g", + "colab_type": "text" + }, + "source": [ + "## 1.2 Why are graphs that don't pass the vertical line test not considered \"functions?\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Gtl20YeDR6x-", + "colab_type": "text" + }, + "source": [ + "Function is defined as a relation between a set of inputs and a set of outputs where each input is related to only one output" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "g21uN62xSKSk", + "colab_type": "text" + }, + "source": [ + "# Functions as Relations" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gwkcV-EMSMNd", + "colab_type": "text" + }, + "source": [ + "## 2.1 Which of the following relations are functions? Why?\n", + "\n", + "\\begin{align}\n", + "\\text{Relation 1: } \\{(1, 2), (3, 2), (1, 3)\\}\n", + "\\\\\n", + "\\text{Relation 2: } \\{(1, 3), (2, 3), (6, 7)\\}\n", + "\\\\\n", + "\\text{Relation 3: } \\{(9, 4), (2, 1), (9, 6)\\}\n", + "\\\\\n", + "\\text{Relation 4: } \\{(6, 2), (8, 3), (6, 4)\\}\n", + "\\\\\n", + "\\text{Relation 5: } \\{(2, 6), (2, 7), (2, 4)\\}\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Dne86CPc2gLO", + "colab_type": "text" + }, + "source": [ + "Relation 2 is a functoin, because each x-value is associated with only one y-value\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "y0U30PrlTAAa", + "colab_type": "text" + }, + "source": [ + "# Functions as a mapping between dimensions\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "pw-OU9qmT5Ua", + "colab_type": "text" + }, + "source": [ + "## 3.1 for the following functions what is the dimensionality of the domain (input) and codomain (range/output)?\n", + "\n", + "\\begin{align}\n", + "m(𝑥_1,𝑥_2,𝑥_3)=(x_1+x_2, x_1+x_3, x_2+x_3)\n", + "\\\\\n", + "\\mathbb{R}^3 to \\mathbb{R}^3\n", + "\\\\\n", + "n(𝑥_1,𝑥_2,𝑥_3,𝑥_4)=(x_2^2 + x_3, x_2x_4)\n", + "\\\\\n", + "\\mathbb{R}^4 to \\mathbb{R}^2\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "k4tKHjdHUevC", + "colab_type": "text" + }, + "source": [ + "## 3.2 Do you think it's possible to create a function that maps from a lower dimensional space to a higher dimensional space? If so, provide an example." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "eESiRcX88QoZ", + "colab_type": "text" + }, + "source": [ + "\\begin{align}\n", + "k(𝑥_1)=(x_1+x_1, x_1x_1)\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "2nEWvwVyVWdW", + "colab_type": "text" + }, + "source": [ + "# Vector Transformations" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1n0-6FsYVcVk", + "colab_type": "text" + }, + "source": [ + "## 4.1 Plug the corresponding unit vectors into each function. Use the output vectors to create a transformation matrix.\n", + "\n", + "\\begin{align}\n", + "p(\\begin{bmatrix}x_1 \\\\ x_2 \\end{bmatrix}) = \\begin{bmatrix} x_1 + 3x_2 \\\\2 x_2 - x_1 \\\\ \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "q(\\begin{bmatrix}x_1 \\\\ x_2 \\\\ x_3\\end{bmatrix}) = \\begin{bmatrix} 4x_1 + x_2 + 2x_3 \\\\2 x_2 - x_1 + 3x_3 \\\\ 5x_1 - 2x_3 + x_2 \\end{bmatrix}\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JoxYW865AU7u", + "colab_type": "text" + }, + "source": [ + "\\begin{align}\n", + "p(\\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}) = \\begin{bmatrix} 1 \\\\ 3 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "p(\\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}) = \\begin{bmatrix} -1 \\\\ 2 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "P = \\begin{bmatrix} 1 & 3 \\\\ -1 & 2 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "q(\\begin{bmatrix} 1 \\\\ 0 \\\\ 0\\end{bmatrix}) = \\begin{bmatrix} 4 \\\\ 1 \\\\ 2\\end {bmatrix}\n", + "\\\\\n", + "\\\\\n", + "q(\\begin{bmatrix} 0 \\\\ 1 \\\\ 0\\end{bmatrix}) = \\begin{bmatrix} -1 \\\\ 2 \\\\ 3\\end {bmatrix}\n", + "\\\\\n", + "\\\\\n", + "q(\\begin{bmatrix} 0 \\\\ 0 \\\\ 1\\end{bmatrix}) = \\begin{bmatrix} 5 \\\\ 1 \\\\ -2\\end {bmatrix}\n", + "\\\\\n", + "\\\\\n", + "Q = \\begin{bmatrix} 4 & 1 & 2 \\\\ -1 & 2 & 3 \\\\ 5 & 1 & -2 \\end{bmatrix}\n", + "\\end{align}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "n5HUOQIxZ2gp", + "colab_type": "text" + }, + "source": [ + "## 4.2 Verify that your transformation matrices are correct by choosing an input matrix and calculating the result both via the traditional functions above and also via vector-matrix multiplication." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "K5US0u1HLyRD", + "colab_type": "text" + }, + "source": [ + "\\begin{align}\n", + "p(\\begin{bmatrix} 2 \\\\ 5 \\end{bmatrix}) = \\begin{bmatrix} 17 \\\\ 8 \\end{bmatrix}\n", + "\\end{align}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "0UANR1IEaVWE", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "c8774fb2-2ba0-480f-fd26-5145cdf2bcfc" + }, + "source": [ + "P = [[1, 3], [-1, 2]]\n", + "vec = [2, 5]\n", + "np.matmul(P,vec)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([17, 8])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 30 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JOs_SMK0NPYA", + "colab_type": "text" + }, + "source": [ + "\\begin{align}\n", + "q(\\begin{bmatrix} 2 \\\\ 1 \\\\ -1 \\end{bmatrix}) = \\begin{bmatrix} 7 \\\\ -3 \\\\ 13\\end{bmatrix}\n", + "\\end{align}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "7W8hwnD4NNQ7", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "2464d024-315f-4ba3-a606-0f29332a303a" + }, + "source": [ + "Q = [[4, 1, 2], [-1, 2, 3], [5, 1, -2]]\n", + "vec1 = [2, 1, -1]\n", + "np.matmul(Q, vec1)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([ 7, -3, 13])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 31 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vEoiri3mak7j", + "colab_type": "text" + }, + "source": [ + "# Eigenvalues and Eigenvectors" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5HY0R4u7anIr", + "colab_type": "text" + }, + "source": [ + "## 5.1 In your own words, give an explanation for the intuition behind eigenvalues and eigenvectors." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "de9N17UsaJhX", + "colab_type": "text" + }, + "source": [ + "Eigenvector is a vector that does not change its orientation during transformation described in a transformation matrix.\n", + "\n", + "Eigenvalue is a scaler which indicates how eigenvector was squished or streched during the transformation." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VdehMwBtatKI", + "colab_type": "text" + }, + "source": [ + "# The Curse of Dimensionality" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4oVrJax-a3SK", + "colab_type": "text" + }, + "source": [ + "## 6.1 What are some of the challenges of working with high dimensional spaces?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BMWAGSgpdP2B", + "colab_type": "text" + }, + "source": [ + "- It is hard for human brain to imagine n-dimensional space, thus it is hard to visualize n-dimentional data\n", + "\n", + "- Extra dimensions are expenssive to process but add less value, at some point it gets less cost effective to \n", + "\n", + "- At a high-dimensional space all data points appear to be more or less equidistant to one another, this harms algoriths that rely upon distance \n", + "\n", + "- When the number of parameters is greater than the number of instances, an extreme risk of overfitting the model occures. The model will no longer fit the signal or phenomen, but the noise or varience" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ZiBJxsZla88c", + "colab_type": "text" + }, + "source": [ + "## 6.2 What is the rule of thumb for how many observations you should have compared to parameters in your model?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ETWnO-17lfrL", + "colab_type": "text" + }, + "source": [ + "Make sure the number of obsevations is five time number of features" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "NZmqdeygbHJx", + "colab_type": "text" + }, + "source": [ + "# Principal Component Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7iEheetpbJdN", + "colab_type": "text" + }, + "source": [ + "## 7.1 Code for loading and cleaning the 2013 national dataset from the [Housing Affordability Data System (HADS)](https://www.huduser.gov/portal/datasets/hads/hads.html) --housing data, can be found below. \n", + "\n", + "## Perform PCA on the processed dataset `national_processed` (Make sure you standardize your data!) and then make a scatterplot of PC1 against PC2. Some of our discussion and work around PCA with this dataset will continue during tomorrow's lecture and assignment.\n", + "\n", + "Not only does this dataset have decent amount columns to begin with (99), but in preparing the data for PCA we have also [one-hot-encoded](https://hackernoon.com/what-is-one-hot-encoding-why-and-when-do-you-have-to-use-it-e3c6186d008f#targetText=One%20hot%20encoding%20is%20a,the%20entry%20in%20the%20dataset.) all of the categorical variables. This has the effect of creating a new column for each individual category of each categorical variable. After processing this dataset has 64738 columns. --Das a lot of columns.\n", + "\n", + "Don't worry too much about the mechanics of one-hot encoding right now, you will learn and experiment with a whole bunch of categorical encoding approaches in unit 2. \n", + "\n", + "The code below will read in the dataset and perform the one-hot encoding of the categorical variables. Start adding your PCA code at the bottom of the provided code." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Us4nNFs02HlD", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 355 + }, + "outputId": "6ed06b36-40a2-4560-d21b-d4ff7f704c6a" + }, + "source": [ + "from urllib.request import urlopen\n", + "from zipfile import ZipFile\n", + "from io import BytesIO\n", + "import os.path\n", + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Read Natinal Data \n", + "national_url = 'https://www.huduser.gov/portal/datasets/hads/hads2013n_ASCII.zip'\n", + "national_file = 'thads2013n.txt'\n", + "\n", + "if os.path.exists(national_file):\n", + " national = pd.read_csv(national_file)\n", + "else: \n", + " z_national = urlopen(national_url)\n", + " zip_national = ZipFile(BytesIO(z_national.read())).extract(national_file)\n", + " national = pd.read_csv(zip_national)\n", + "\n", + "print(national.shape)\n", + "national.head()" + ], + "execution_count": 5, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(64535, 99)\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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CONTROLAGE1METRO3REGIONLMEDFMRL30L50L80IPOVBEDRMSBUILTSTATUSTYPEVALUEVACANCYTENURENUNITSROOMSWEIGHTPERZINC2ZADEQZSMHCSTRUCTURETYPEOWNRENTUTILITYOTHERCOSTCOST06COST12COST08COSTMEDTOTSALASSISTEDGLMEDGL30GL50GL80APLMEDABL30...COST08RELPOVCATCOST08RELFMRPCTCOST08RELFMRCATCOST12RELAMIPCTCOST12RELAMICATCOST12RELPOVPCTCOST12RELPOVCATCOST12RELFMRPCTCOST12RELFMRCATCOSTMedRELAMIPCTCOSTMedRELAMICATCOSTMedRELPOVPCTCOSTMedRELPOVCATCOSTMedRELFMRPCTCOSTMedRELFMRCATFMTZADEQFMTMETRO3FMTBUILTFMTSTRUCTURETYPEFMTBEDRMSFMTOWNRENTFMTCOST06RELPOVCATFMTCOST08RELPOVCATFMTCOST12RELPOVCATFMTCOSTMEDRELPOVCATFMTINCRELPOVCATFMTCOST06RELFMRCATFMTCOST08RELFMRCATFMTCOST12RELFMRCATFMTCOSTMEDRELFMRCATFMTINCRELFMRCATFMTCOST06RELAMICATFMTCOST08RELAMICATFMTCOST12RELAMICATFMTCOSTMEDRELAMICATFMTINCRELAMICATFMTASSISTEDFMTBURDENFMTREGIONFMTSTATUS
0'100003130103'82'3''1'737389561573826213403221106722006'1'140000-6'1'163117.394239118021'1'5331'1'169.000000213.750000648.588189803.050535696.905247615.1567120-97373815738262134032251616.620234.571429...472.898038248.4026352290.250487484.001102237.0776242222.339102464.3469362'1 Adequate''-5''2000-2009''1 Single Family''2 2BR''1 Owner''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''3 150-200% Poverty''2 50.1 - 100% FMR''2 50.1 - 100% FMR''2 50.1 - 100% FMR''2 50.1 - 100% FMR''1 LTE 50% FMR''2 30 - 50% AMI''2 30 - 50% AMI''2 30 - 50% AMI''2 30 - 50% AMI''2 30 - 50% AMI''.''2 30% to 50%''-5''-5'
1'100006110249'50'5''3'5584611001716528604457442421841980'1'1130000-6'1'162150.7255444122961'1'4871'1'245.33333358.3333331167.6407811669.6434051324.6712181058.988479123000-95584617165286044574455846.019911.400000...4120.4246563103.0940636275.7689994151.785764365.3884684174.909320396.2716802'1 Adequate''-5''1980-1989''1 Single Family''4 4BR+''1 Owner''3 150-200% Poverty''4 200%+ Poverty''4 200%+ Poverty''3 150-200% Poverty''4 200%+ Poverty''3 GT FMR''3 GT FMR''3 GT FMR''2 50.1 - 100% FMR''3 GT FMR''4 60 - 80% AMI''4 60 - 80% AMI''6 100 - 120% AMI''4 60 - 80% AMI''7 120% AMI +''.''1 Less than 30%''-5''-5'
2'100006370140'53'5''3'5584611001375022897366141547041985'1'1150000-6'1'172213.789404227974'1'14051'1'159.00000037.5000001193.3932091772.6270061374.5821751068.02516828000-95584613750228973661444676.819937.500000...4124.9620163109.4529056458.3392394161.147910365.9464494276.153890497.0931972'1 Adequate''-5''1980-1989''1 Single Family''4 4BR+''1 Owner''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''3 150-200% Poverty''3 GT FMR''3 GT FMR''3 GT FMR''2 50.1 - 100% FMR''2 50.1 - 100% FMR''4 60 - 80% AMI''5 80 - 100% AMI''6 100 - 120% AMI''4 60 - 80% AMI''4 60 - 80% AMI''.''3 50% or More''-5''-5'
3'100006520140'67'5''3'558469491375022897366141396431985'1'1200000-6'1'162364.585097232220'1'2791'1'179.00000070.6666671578.8576122351.1693411820.4429001411.7002240-95584613750228973661444676.817875.000000...4191.8274923161.9267097673.4945124247.752301397.2248015404.3827634148.7566103'1 Adequate''-5''1980-1989''1 Single Family''3 3BR''1 Owner''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''3 GT FMR''3 GT FMR''3 GT FMR''3 GT FMR''2 50.1 - 100% FMR''6 100 - 120% AMI''7 120% AMI +''7 120% AMI +''5 80 - 100% AMI''4 60 - 80% AMI''.''1 Less than 30%''-5''-5'
4'100007130148'26'1''3'609917371480124628394211549221980'1'1-6-6'2'10042314.524902296874'1'7595'2'146.00000012.500000759.000000759.000000759.000000759.0000009690006099114801246283942148792.816651.125000...3102.985075355.3087073195.9721153102.985075355.3087073195.9721153102.9850753'1 Adequate''Central City''1980-1989''5 50+ units''2 2BR''2 Renter''3 150-200% Poverty''3 150-200% Poverty''3 150-200% Poverty''3 150-200% Poverty''4 200%+ Poverty''3 GT FMR''3 GT FMR''3 GT FMR''3 GT FMR''3 GT FMR''3 50 - 60% AMI''3 50 - 60% AMI''3 50 - 60% AMI''3 50 - 60% AMI''7 120% AMI +''0 Not Assisted''1 Less than 30%''-5''-5'
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5 rows × 99 columns

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" + ], + "text/plain": [ + " CONTROL AGE1 METRO3 ... FMTBURDEN FMTREGION FMTSTATUS\n", + "0 '100003130103' 82 '3' ... '2 30% to 50%' '-5' '-5'\n", + "1 '100006110249' 50 '5' ... '1 Less than 30%' '-5' '-5'\n", + "2 '100006370140' 53 '5' ... '3 50% or More' '-5' '-5'\n", + "3 '100006520140' 67 '5' ... '1 Less than 30%' '-5' '-5'\n", + "4 '100007130148' 26 '1' ... '1 Less than 30%' '-5' '-5'\n", + "\n", + "[5 rows x 99 columns]" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 5 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "O5zrMTud2qFU", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 221 + }, + "outputId": "3b322e7c-c370-4b18-8774-06c7b345e841" + }, + "source": [ + "# Look at datatypes\n", + "# a lot of object datatypes even though they seem to be strings of numbers.\n", + "national.dtypes" + ], + "execution_count": 6, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "CONTROL object\n", + "AGE1 int64\n", + "METRO3 object\n", + "REGION object\n", + "LMED int64\n", + " ... \n", + "FMTINCRELAMICAT object\n", + "FMTASSISTED object\n", + "FMTBURDEN object\n", + "FMTREGION object\n", + "FMTSTATUS object\n", + "Length: 99, dtype: object" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 6 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "yIrOjVmd2yLz", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "576da546-8735-467c-b5ad-db8078842dba" + }, + "source": [ + "# check for null values\n", + "national.isnull().sum().any()" + ], + "execution_count": 7, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "False" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 7 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "2u9tdmwX3KL_", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "f8dd4d1e-0e5a-4ab4-baab-a2c7a9e040a1" + }, + "source": [ + "# check for number of categorical vs numeric columns\n", + "cat_cols = national.columns[national.dtypes=='object']\n", + "num_cols = national.columns[national.dtypes!='object']\n", + "\n", + "print(f'{len(cat_cols)} categorical columns')\n", + "print(f'{len(num_cols)} numerical columns')" + ], + "execution_count": 8, + "outputs": [ + { + "output_type": "stream", + "text": [ + "32 categorical columns\n", + "67 numerical columns\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "UMHOtOs_3gcL", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 221 + }, + "outputId": "a20f31b6-522e-4f40-d082-c0817dab2a48" + }, + "source": [ + "# We're making a copy of our data in case we mess something up.\n", + "national_processed = national.copy()\n", + "\n", + "# Categorically Encode our Variables:\n", + "# They need to all be numeric before we do PCA.\n", + "# https://pbpython.com/categorical-encoding.html\n", + "\n", + "# Cast categorical columns to \"category\" data type\n", + "national_processed[cat_cols] = national_processed[cat_cols].astype('category')\n", + "\n", + "national_processed.dtypes" + ], + "execution_count": 9, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "CONTROL category\n", + "AGE1 int64\n", + "METRO3 category\n", + "REGION category\n", + "LMED int64\n", + " ... \n", + "FMTINCRELAMICAT category\n", + "FMTASSISTED category\n", + "FMTBURDEN category\n", + "FMTREGION category\n", + "FMTSTATUS category\n", + "Length: 99, dtype: object" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 9 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "ymxU-aPtQ1eq", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 270 + }, + "outputId": "933f0691-7015-4da0-d6f7-edccd97b085d" + }, + "source": [ + "# Replace all category cell values with their numeric category codes\n", + "for col in cat_cols:\n", + " national_processed[col] = national_processed[col].cat.codes\n", + "\n", + "print(national_processed.shape)\n", + "national_processed.head()" + ], + "execution_count": 10, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(64535, 99)\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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        jsSuffixRegExp = /\.js$/,
        currDirRegExp = /^\.\//,
        op = Object.prototype,
        ostring = op.toString,
        hasOwn = op.hasOwnProperty,
        ap = Array.prototype,
        isBrowser = !!(typeof window !== 'undefined' && typeof navigator !== 'undefined' && window.document),
        isWebWorker = !isBrowser && typeof importScripts !== 'undefined',
        //PS3 indicates loaded and complete, but need to wait for complete
        //specifically. Sequence is 'loading', 'loaded', execution,
        // then 'complete'. The UA check is unfortunate, but not sure how
        //to feature test w/o causing perf issues.
        readyRegExp = isBrowser && navigator.platform === 'PLAYSTATION 3' ?
                      /^complete$/ : /^(complete|loaded)$/,
        defContextName = '_',
        //Oh the tragedy, detecting opera. See the usage of isOpera for reason.
        isOpera = typeof opera !== 'undefined' && opera.toString() === '[object Opera]',
        contexts = {},
        cfg = {},
        globalDefQueue = [],
        useInteractive = false;

    function isFunction(it) {
        return ostring.call(it) === '[object Function]';
    }

    function isArray(it) {
        return ostring.call(it) === '[object Array]';
    }

    /**
     * Helper function for iterating over an array. If the func returns
     * a true value, it will break out of the loop.
     */
    function each(ary, func) {
        if (ary) {
            var i;
            for (i = 0; i < ary.length; i += 1) {
                if (ary[i] && func(ary[i], i, ary)) {
                    break;
                }
            }
        }
    }

    /**
     * Helper function for iterating over an array backwards. If the func
     * returns a true value, it will break out of the loop.
     */
    function eachReverse(ary, func) {
        if (ary) {
            var i;
            for (i = ary.length - 1; i > -1; i -= 1) {
                if (ary[i] && func(ary[i], i, ary)) {
                    break;
                }
            }
        }
    }

    function hasProp(obj, prop) {
        return hasOwn.call(obj, prop);
    }

    function getOwn(obj, prop) {
        return hasProp(obj, prop) && obj[prop];
    }

    /**
     * Cycles over properties in an object and calls a function for each
     * property value. If the function returns a truthy value, then the
     * iteration is stopped.
     */
    function eachProp(obj, func) {
        var prop;
        for (prop in obj) {
            if (hasProp(obj, prop)) {
                if (func(obj[prop], prop)) {
                    break;
                }
            }
        }
    }

    /**
     * Simple function to mix in properties from source into target,
     * but only if target does not already have a property of the same name.
     */
    function mixin(target, source, force, deepStringMixin) {
        if (source) {
            eachProp(source, function (value, prop) {
                if (force || !hasProp(target, prop)) {
                    if (deepStringMixin && typeof value === 'object' && value &&
                        !isArray(value) && !isFunction(value) &&
                        !(value instanceof RegExp)) {

                        if (!target[prop]) {
                            target[prop] = {};
                        }
                        mixin(target[prop], value, force, deepStringMixin);
                    } else {
                        target[prop] = value;
                    }
                }
            });
        }
        return target;
    }

    //Similar to Function.prototype.bind, but the 'this' object is specified
    //first, since it is easier to read/figure out what 'this' will be.
    function bind(obj, fn) {
        return function () {
            return fn.apply(obj, arguments);
        };
    }

    function scripts() {
        return document.getElementsByTagName('script');
    }

    function defaultOnError(err) {
        throw err;
    }

    //Allow getting a global that is expressed in
    //dot notation, like 'a.b.c'.
    function getGlobal(value) {
        if (!value) {
            return value;
        }
        var g = global;
        each(value.split('.'), function (part) {
            g = g[part];
        });
        return g;
    }

    /**
     * Constructs an error with a pointer to an URL with more information.
     * @param {String} id the error ID that maps to an ID on a web page.
     * @param {String} message human readable error.
     * @param {Error} [err] the original error, if there is one.
     *
     * @returns {Error}
     */
    function makeError(id, msg, err, requireModules) {
        var e = new Error(msg + '\nhttp://requirejs.org/docs/errors.html#' + id);
        e.requireType = id;
        e.requireModules = requireModules;
        if (err) {
            e.originalError = err;
        }
        return e;
    }

    if (typeof define !== 'undefined') {
        //If a define is already in play via another AMD loader,
        //do not overwrite.
        return;
    }

    if (typeof requirejs !== 'undefined') {
        if (isFunction(requirejs)) {
            //Do not overwrite an existing requirejs instance.
            return;
        }
        cfg = requirejs;
        requirejs = undefined;
    }

    //Allow for a require config object
    if (typeof require !== 'undefined' && !isFunction(require)) {
        //assume it is a config object.
        cfg = require;
        require = undefined;
    }

    function newContext(contextName) {
        var inCheckLoaded, Module, context, handlers,
            checkLoadedTimeoutId,
            config = {
                //Defaults. Do not set a default for map
                //config to speed up normalize(), which
                //will run faster if there is no default.
                waitSeconds: 7,
                baseUrl: './',
                paths: {},
                bundles: {},
                pkgs: {},
                shim: {},
                config: {}
            },
            registry = {},
            //registry of just enabled modules, to speed
            //cycle breaking code when lots of modules
            //are registered, but not activated.
            enabledRegistry = {},
            undefEvents = {},
            defQueue = [],
            defined = {},
            urlFetched = {},
            bundlesMap = {},
            requireCounter = 1,
            unnormalizedCounter = 1;

        /**
         * Trims the . and .. from an array of path segments.
         * It will keep a leading path segment if a .. will become
         * the first path segment, to help with module name lookups,
         * which act like paths, but can be remapped. But the end result,
         * all paths that use this function should look normalized.
         * NOTE: this method MODIFIES the input array.
         * @param {Array} ary the array of path segments.
         */
        function trimDots(ary) {
            var i, part;
            for (i = 0; i < ary.length; i++) {
                part = ary[i];
                if (part === '.') {
                    ary.splice(i, 1);
                    i -= 1;
                } else if (part === '..') {
                    // If at the start, or previous value is still ..,
                    // keep them so that when converted to a path it may
                    // still work when converted to a path, even though
                    // as an ID it is less than ideal. In larger point
                    // releases, may be better to just kick out an error.
                    if (i === 0 || (i === 1 && ary[2] === '..') || ary[i - 1] === '..') {
                        continue;
                    } else if (i > 0) {
                        ary.splice(i - 1, 2);
                        i -= 2;
                    }
                }
            }
        }

        /**
         * Given a relative module name, like ./something, normalize it to
         * a real name that can be mapped to a path.
         * @param {String} name the relative name
         * @param {String} baseName a real name that the name arg is relative
         * to.
         * @param {Boolean} applyMap apply the map config to the value. Should
         * only be done if this normalization is for a dependency ID.
         * @returns {String} normalized name
         */
        function normalize(name, baseName, applyMap) {
            var pkgMain, mapValue, nameParts, i, j, nameSegment, lastIndex,
                foundMap, foundI, foundStarMap, starI, normalizedBaseParts,
                baseParts = (baseName && baseName.split('/')),
                map = config.map,
                starMap = map && map['*'];

            //Adjust any relative paths.
            if (name) {
                name = name.split('/');
                lastIndex = name.length - 1;

                // If wanting node ID compatibility, strip .js from end
                // of IDs. Have to do this here, and not in nameToUrl
                // because node allows either .js or non .js to map
                // to same file.
                if (config.nodeIdCompat && jsSuffixRegExp.test(name[lastIndex])) {
                    name[lastIndex] = name[lastIndex].replace(jsSuffixRegExp, '');
                }

                // Starts with a '.' so need the baseName
                if (name[0].charAt(0) === '.' && baseParts) {
                    //Convert baseName to array, and lop off the last part,
                    //so that . matches that 'directory' and not name of the baseName's
                    //module. For instance, baseName of 'one/two/three', maps to
                    //'one/two/three.js', but we want the directory, 'one/two' for
                    //this normalization.
                    normalizedBaseParts = baseParts.slice(0, baseParts.length - 1);
                    name = normalizedBaseParts.concat(name);
                }

                trimDots(name);
                name = name.join('/');
            }

            //Apply map config if available.
            if (applyMap && map && (baseParts || starMap)) {
                nameParts = name.split('/');

                outerLoop: for (i = nameParts.length; i > 0; i -= 1) {
                    nameSegment = nameParts.slice(0, i).join('/');

                    if (baseParts) {
                        //Find the longest baseName segment match in the config.
                        //So, do joins on the biggest to smallest lengths of baseParts.
                        for (j = baseParts.length; j > 0; j -= 1) {
                            mapValue = getOwn(map, baseParts.slice(0, j).join('/'));

                            //baseName segment has config, find if it has one for
                            //this name.
                            if (mapValue) {
                                mapValue = getOwn(mapValue, nameSegment);
                                if (mapValue) {
                                    //Match, update name to the new value.
                                    foundMap = mapValue;
                                    foundI = i;
                                    break outerLoop;
                                }
                            }
                        }
                    }

                    //Check for a star map match, but just hold on to it,
                    //if there is a shorter segment match later in a matching
                    //config, then favor over this star map.
                    if (!foundStarMap && starMap && getOwn(starMap, nameSegment)) {
                        foundStarMap = getOwn(starMap, nameSegment);
                        starI = i;
                    }
                }

                if (!foundMap && foundStarMap) {
                    foundMap = foundStarMap;
                    foundI = starI;
                }

                if (foundMap) {
                    nameParts.splice(0, foundI, foundMap);
                    name = nameParts.join('/');
                }
            }

            // If the name points to a package's name, use
            // the package main instead.
            pkgMain = getOwn(config.pkgs, name);

            return pkgMain ? pkgMain : name;
        }

        function removeScript(name) {
            if (isBrowser) {
                each(scripts(), function (scriptNode) {
                    if (scriptNode.getAttribute('data-requiremodule') === name &&
                            scriptNode.getAttribute('data-requirecontext') === context.contextName) {
                        scriptNode.parentNode.removeChild(scriptNode);
                        return true;
                    }
                });
            }
        }

        function hasPathFallback(id) {
            var pathConfig = getOwn(config.paths, id);
            if (pathConfig && isArray(pathConfig) && pathConfig.length > 1) {
                //Pop off the first array value, since it failed, and
                //retry
                pathConfig.shift();
                context.require.undef(id);

                //Custom require that does not do map translation, since
                //ID is "absolute", already mapped/resolved.
                context.makeRequire(null, {
                    skipMap: true
                })([id]);

                return true;
            }
        }

        //Turns a plugin!resource to [plugin, resource]
        //with the plugin being undefined if the name
        //did not have a plugin prefix.
        function splitPrefix(name) {
            var prefix,
                index = name ? name.indexOf('!') : -1;
            if (index > -1) {
                prefix = name.substring(0, index);
                name = name.substring(index + 1, name.length);
            }
            return [prefix, name];
        }

        /**
         * Creates a module mapping that includes plugin prefix, module
         * name, and path. If parentModuleMap is provided it will
         * also normalize the name via require.normalize()
         *
         * @param {String} name the module name
         * @param {String} [parentModuleMap] parent module map
         * for the module name, used to resolve relative names.
         * @param {Boolean} isNormalized: is the ID already normalized.
         * This is true if this call is done for a define() module ID.
         * @param {Boolean} applyMap: apply the map config to the ID.
         * Should only be true if this map is for a dependency.
         *
         * @returns {Object}
         */
        function makeModuleMap(name, parentModuleMap, isNormalized, applyMap) {
            var url, pluginModule, suffix, nameParts,
                prefix = null,
                parentName = parentModuleMap ? parentModuleMap.name : null,
                originalName = name,
                isDefine = true,
                normalizedName = '';

            //If no name, then it means it is a require call, generate an
            //internal name.
            if (!name) {
                isDefine = false;
                name = '_@r' + (requireCounter += 1);
            }

            nameParts = splitPrefix(name);
            prefix = nameParts[0];
            name = nameParts[1];

            if (prefix) {
                prefix = normalize(prefix, parentName, applyMap);
                pluginModule = getOwn(defined, prefix);
            }

            //Account for relative paths if there is a base name.
            if (name) {
                if (prefix) {
                    if (pluginModule && pluginModule.normalize) {
                        //Plugin is loaded, use its normalize method.
                        normalizedName = pluginModule.normalize(name, function (name) {
                            return normalize(name, parentName, applyMap);
                        });
                    } else {
                        // If nested plugin references, then do not try to
                        // normalize, as it will not normalize correctly. This
                        // places a restriction on resourceIds, and the longer
                        // term solution is not to normalize until plugins are
                        // loaded and all normalizations to allow for async
                        // loading of a loader plugin. But for now, fixes the
                        // common uses. Details in #1131
                        normalizedName = name.indexOf('!') === -1 ?
                                         normalize(name, parentName, applyMap) :
                                         name;
                    }
                } else {
                    //A regular module.
                    normalizedName = normalize(name, parentName, applyMap);

                    //Normalized name may be a plugin ID due to map config
                    //application in normalize. The map config values must
                    //already be normalized, so do not need to redo that part.
                    nameParts = splitPrefix(normalizedName);
                    prefix = nameParts[0];
                    normalizedName = nameParts[1];
                    isNormalized = true;

                    url = context.nameToUrl(normalizedName);
                }
            }

            //If the id is a plugin id that cannot be determined if it needs
            //normalization, stamp it with a unique ID so two matching relative
            //ids that may conflict can be separate.
            suffix = prefix && !pluginModule && !isNormalized ?
                     '_unnormalized' + (unnormalizedCounter += 1) :
                     '';

            return {
                prefix: prefix,
                name: normalizedName,
                parentMap: parentModuleMap,
                unnormalized: !!suffix,
                url: url,
                originalName: originalName,
                isDefine: isDefine,
                id: (prefix ?
                        prefix + '!' + normalizedName :
                        normalizedName) + suffix
            };
        }

        function getModule(depMap) {
            var id = depMap.id,
                mod = getOwn(registry, id);

            if (!mod) {
                mod = registry[id] = new context.Module(depMap);
            }

            return mod;
        }

        function on(depMap, name, fn) {
            var id = depMap.id,
                mod = getOwn(registry, id);

            if (hasProp(defined, id) &&
                    (!mod || mod.defineEmitComplete)) {
                if (name === 'defined') {
                    fn(defined[id]);
                }
            } else {
                mod = getModule(depMap);
                if (mod.error && name === 'error') {
                    fn(mod.error);
                } else {
                    mod.on(name, fn);
                }
            }
        }

        function onError(err, errback) {
            var ids = err.requireModules,
                notified = false;

            if (errback) {
                errback(err);
            } else {
                each(ids, function (id) {
                    var mod = getOwn(registry, id);
                    if (mod) {
                        //Set error on module, so it skips timeout checks.
                        mod.error = err;
                        if (mod.events.error) {
                            notified = true;
                            mod.emit('error', err);
                        }
                    }
                });

                if (!notified) {
                    req.onError(err);
                }
            }
        }

        /**
         * Internal method to transfer globalQueue items to this context's
         * defQueue.
         */
        function takeGlobalQueue() {
            //Push all the globalDefQueue items into the context's defQueue
            if (globalDefQueue.length) {
                each(globalDefQueue, function(queueItem) {
                    var id = queueItem[0];
                    if (typeof id === 'string') {
                        context.defQueueMap[id] = true;
                    }
                    defQueue.push(queueItem);
                });
                globalDefQueue = [];
            }
        }

        handlers = {
            'require': function (mod) {
                if (mod.require) {
                    return mod.require;
                } else {
                    return (mod.require = context.makeRequire(mod.map));
                }
            },
            'exports': function (mod) {
                mod.usingExports = true;
                if (mod.map.isDefine) {
                    if (mod.exports) {
                        return (defined[mod.map.id] = mod.exports);
                    } else {
                        return (mod.exports = defined[mod.map.id] = {});
                    }
                }
            },
            'module': function (mod) {
                if (mod.module) {
                    return mod.module;
                } else {
                    return (mod.module = {
                        id: mod.map.id,
                        uri: mod.map.url,
                        config: function () {
                            return getOwn(config.config, mod.map.id) || {};
                        },
                        exports: mod.exports || (mod.exports = {})
                    });
                }
            }
        };

        function cleanRegistry(id) {
            //Clean up machinery used for waiting modules.
            delete registry[id];
            delete enabledRegistry[id];
        }

        function breakCycle(mod, traced, processed) {
            var id = mod.map.id;

            if (mod.error) {
                mod.emit('error', mod.error);
            } else {
                traced[id] = true;
                each(mod.depMaps, function (depMap, i) {
                    var depId = depMap.id,
                        dep = getOwn(registry, depId);

                    //Only force things that have not completed
                    //being defined, so still in the registry,
                    //and only if it has not been matched up
                    //in the module already.
                    if (dep && !mod.depMatched[i] && !processed[depId]) {
                        if (getOwn(traced, depId)) {
                            mod.defineDep(i, defined[depId]);
                            mod.check(); //pass false?
                        } else {
                            breakCycle(dep, traced, processed);
                        }
                    }
                });
                processed[id] = true;
            }
        }

        function checkLoaded() {
            var err, usingPathFallback,
                waitInterval = config.waitSeconds * 1000,
                //It is possible to disable the wait interval by using waitSeconds of 0.
                expired = waitInterval && (context.startTime + waitInterval) < new Date().getTime(),
                noLoads = [],
                reqCalls = [],
                stillLoading = false,
                needCycleCheck = true;

            //Do not bother if this call was a result of a cycle break.
            if (inCheckLoaded) {
                return;
            }

            inCheckLoaded = true;

            //Figure out the state of all the modules.
            eachProp(enabledRegistry, function (mod) {
                var map = mod.map,
                    modId = map.id;

                //Skip things that are not enabled or in error state.
                if (!mod.enabled) {
                    return;
                }

                if (!map.isDefine) {
                    reqCalls.push(mod);
                }

                if (!mod.error) {
                    //If the module should be executed, and it has not
                    //been inited and time is up, remember it.
                    if (!mod.inited && expired) {
                        if (hasPathFallback(modId)) {
                            usingPathFallback = true;
                            stillLoading = true;
                        } else {
                            noLoads.push(modId);
                            removeScript(modId);
                        }
                    } else if (!mod.inited && mod.fetched && map.isDefine) {
                        stillLoading = true;
                        if (!map.prefix) {
                            //No reason to keep looking for unfinished
                            //loading. If the only stillLoading is a
                            //plugin resource though, keep going,
                            //because it may be that a plugin resource
                            //is waiting on a non-plugin cycle.
                            return (needCycleCheck = false);
                        }
                    }
                }
            });

            if (expired && noLoads.length) {
                //If wait time expired, throw error of unloaded modules.
                err = makeError('timeout', 'Load timeout for modules: ' + noLoads, null, noLoads);
                err.contextName = context.contextName;
                return onError(err);
            }

            //Not expired, check for a cycle.
            if (needCycleCheck) {
                each(reqCalls, function (mod) {
                    breakCycle(mod, {}, {});
                });
            }

            //If still waiting on loads, and the waiting load is something
            //other than a plugin resource, or there are still outstanding
            //scripts, then just try back later.
            if ((!expired || usingPathFallback) && stillLoading) {
                //Something is still waiting to load. Wait for it, but only
                //if a timeout is not already in effect.
                if ((isBrowser || isWebWorker) && !checkLoadedTimeoutId) {
                    checkLoadedTimeoutId = setTimeout(function () {
                        checkLoadedTimeoutId = 0;
                        checkLoaded();
                    }, 50);
                }
            }

            inCheckLoaded = false;
        }

        Module = function (map) {
            this.events = getOwn(undefEvents, map.id) || {};
            this.map = map;
            this.shim = getOwn(config.shim, map.id);
            this.depExports = [];
            this.depMaps = [];
            this.depMatched = [];
            this.pluginMaps = {};
            this.depCount = 0;

            /* this.exports this.factory
               this.depMaps = [],
               this.enabled, this.fetched
            */
        };

        Module.prototype = {
            init: function (depMaps, factory, errback, options) {
                options = options || {};

                //Do not do more inits if already done. Can happen if there
                //are multiple define calls for the same module. That is not
                //a normal, common case, but it is also not unexpected.
                if (this.inited) {
                    return;
                }

                this.factory = factory;

                if (errback) {
                    //Register for errors on this module.
                    this.on('error', errback);
                } else if (this.events.error) {
                    //If no errback already, but there are error listeners
                    //on this module, set up an errback to pass to the deps.
                    errback = bind(this, function (err) {
                        this.emit('error', err);
                    });
                }

                //Do a copy of the dependency array, so that
                //source inputs are not modified. For example
                //"shim" deps are passed in here directly, and
                //doing a direct modification of the depMaps array
                //would affect that config.
                this.depMaps = depMaps && depMaps.slice(0);

                this.errback = errback;

                //Indicate this module has be initialized
                this.inited = true;

                this.ignore = options.ignore;

                //Could have option to init this module in enabled mode,
                //or could have been previously marked as enabled. However,
                //the dependencies are not known until init is called. So
                //if enabled previously, now trigger dependencies as enabled.
                if (options.enabled || this.enabled) {
                    //Enable this module and dependencies.
                    //Will call this.check()
                    this.enable();
                } else {
                    this.check();
                }
            },

            defineDep: function (i, depExports) {
                //Because of cycles, defined callback for a given
                //export can be called more than once.
                if (!this.depMatched[i]) {
                    this.depMatched[i] = true;
                    this.depCount -= 1;
                    this.depExports[i] = depExports;
                }
            },

            fetch: function () {
                if (this.fetched) {
                    return;
                }
                this.fetched = true;

                context.startTime = (new Date()).getTime();

                var map = this.map;

                //If the manager is for a plugin managed resource,
                //ask the plugin to load it now.
                if (this.shim) {
                    context.makeRequire(this.map, {
                        enableBuildCallback: true
                    })(this.shim.deps || [], bind(this, function () {
                        return map.prefix ? this.callPlugin() : this.load();
                    }));
                } else {
                    //Regular dependency.
                    return map.prefix ? this.callPlugin() : this.load();
                }
            },

            load: function () {
                var url = this.map.url;

                //Regular dependency.
                if (!urlFetched[url]) {
                    urlFetched[url] = true;
                    context.load(this.map.id, url);
                }
            },

            /**
             * Checks if the module is ready to define itself, and if so,
             * define it.
             */
            check: function () {
                if (!this.enabled || this.enabling) {
                    return;
                }

                var err, cjsModule,
                    id = this.map.id,
                    depExports = this.depExports,
                    exports = this.exports,
                    factory = this.factory;

                if (!this.inited) {
                    // Only fetch if not already in the defQueue.
                    if (!hasProp(context.defQueueMap, id)) {
                        this.fetch();
                    }
                } else if (this.error) {
                    this.emit('error', this.error);
                } else if (!this.defining) {
                    //The factory could trigger another require call
                    //that would result in checking this module to
                    //define itself again. If already in the process
                    //of doing that, skip this work.
                    this.defining = true;

                    if (this.depCount < 1 && !this.defined) {
                        if (isFunction(factory)) {
                            try {
                                exports = context.execCb(id, factory, depExports, exports);
                            } catch (e) {
                                err = e;
                            }

                            // Favor return value over exports. If node/cjs in play,
                            // then will not have a return value anyway. Favor
                            // module.exports assignment over exports object.
                            if (this.map.isDefine && exports === undefined) {
                                cjsModule = this.module;
                                if (cjsModule) {
                                    exports = cjsModule.exports;
                                } else if (this.usingExports) {
                                    //exports already set the defined value.
                                    exports = this.exports;
                                }
                            }

                            if (err) {
                                // If there is an error listener, favor passing
                                // to that instead of throwing an error. However,
                                // only do it for define()'d  modules. require
                                // errbacks should not be called for failures in
                                // their callbacks (#699). However if a global
                                // onError is set, use that.
                                if ((this.events.error && this.map.isDefine) ||
                                    req.onError !== defaultOnError) {
                                    err.requireMap = this.map;
                                    err.requireModules = this.map.isDefine ? [this.map.id] : null;
                                    err.requireType = this.map.isDefine ? 'define' : 'require';
                                    return onError((this.error = err));
                                } else if (typeof console !== 'undefined' &&
                                           console.error) {
                                    // Log the error for debugging. If promises could be
                                    // used, this would be different, but making do.
                                    console.error(err);
                                } else {
                                    // Do not want to completely lose the error. While this
                                    // will mess up processing and lead to similar results
                                    // as bug 1440, it at least surfaces the error.
                                    req.onError(err);
                                }
                            }
                        } else {
                            //Just a literal value
                            exports = factory;
                        }

                        this.exports = exports;

                        if (this.map.isDefine && !this.ignore) {
                            defined[id] = exports;

                            if (req.onResourceLoad) {
                                var resLoadMaps = [];
                                each(this.depMaps, function (depMap) {
                                    resLoadMaps.push(depMap.normalizedMap || depMap);
                                });
                                req.onResourceLoad(context, this.map, resLoadMaps);
                            }
                        }

                        //Clean up
                        cleanRegistry(id);

                        this.defined = true;
                    }

                    //Finished the define stage. Allow calling check again
                    //to allow define notifications below in the case of a
                    //cycle.
                    this.defining = false;

                    if (this.defined && !this.defineEmitted) {
                        this.defineEmitted = true;
                        this.emit('defined', this.exports);
                        this.defineEmitComplete = true;
                    }

                }
            },

            callPlugin: function () {
                var map = this.map,
                    id = map.id,
                    //Map already normalized the prefix.
                    pluginMap = makeModuleMap(map.prefix);

                //Mark this as a dependency for this plugin, so it
                //can be traced for cycles.
                this.depMaps.push(pluginMap);

                on(pluginMap, 'defined', bind(this, function (plugin) {
                    var load, normalizedMap, normalizedMod,
                        bundleId = getOwn(bundlesMap, this.map.id),
                        name = this.map.name,
                        parentName = this.map.parentMap ? this.map.parentMap.name : null,
                        localRequire = context.makeRequire(map.parentMap, {
                            enableBuildCallback: true
                        });

                    //If current map is not normalized, wait for that
                    //normalized name to load instead of continuing.
                    if (this.map.unnormalized) {
                        //Normalize the ID if the plugin allows it.
                        if (plugin.normalize) {
                            name = plugin.normalize(name, function (name) {
                                return normalize(name, parentName, true);
                            }) || '';
                        }

                        //prefix and name should already be normalized, no need
                        //for applying map config again either.
                        normalizedMap = makeModuleMap(map.prefix + '!' + name,
                                                      this.map.parentMap);
                        on(normalizedMap,
                            'defined', bind(this, function (value) {
                                this.map.normalizedMap = normalizedMap;
                                this.init([], function () { return value; }, null, {
                                    enabled: true,
                                    ignore: true
                                });
                            }));

                        normalizedMod = getOwn(registry, normalizedMap.id);
                        if (normalizedMod) {
                            //Mark this as a dependency for this plugin, so it
                            //can be traced for cycles.
                            this.depMaps.push(normalizedMap);

                            if (this.events.error) {
                                normalizedMod.on('error', bind(this, function (err) {
                                    this.emit('error', err);
                                }));
                            }
                            normalizedMod.enable();
                        }

                        return;
                    }

                    //If a paths config, then just load that file instead to
                    //resolve the plugin, as it is built into that paths layer.
                    if (bundleId) {
                        this.map.url = context.nameToUrl(bundleId);
                        this.load();
                        return;
                    }

                    load = bind(this, function (value) {
                        this.init([], function () { return value; }, null, {
                            enabled: true
                        });
                    });

                    load.error = bind(this, function (err) {
                        this.inited = true;
                        this.error = err;
                        err.requireModules = [id];

                        //Remove temp unnormalized modules for this module,
                        //since they will never be resolved otherwise now.
                        eachProp(registry, function (mod) {
                            if (mod.map.id.indexOf(id + '_unnormalized') === 0) {
                                cleanRegistry(mod.map.id);
                            }
                        });

                        onError(err);
                    });

                    //Allow plugins to load other code without having to know the
                    //context or how to 'complete' the load.
                    load.fromText = bind(this, function (text, textAlt) {
                        /*jslint evil: true */
                        var moduleName = map.name,
                            moduleMap = makeModuleMap(moduleName),
                            hasInteractive = useInteractive;

                        //As of 2.1.0, support just passing the text, to reinforce
                        //fromText only being called once per resource. Still
                        //support old style of passing moduleName but discard
                        //that moduleName in favor of the internal ref.
                        if (textAlt) {
                            text = textAlt;
                        }

                        //Turn off interactive script matching for IE for any define
                        //calls in the text, then turn it back on at the end.
                        if (hasInteractive) {
                            useInteractive = false;
                        }

                        //Prime the system by creating a module instance for
                        //it.
                        getModule(moduleMap);

                        //Transfer any config to this other module.
                        if (hasProp(config.config, id)) {
                            config.config[moduleName] = config.config[id];
                        }

                        try {
                            req.exec(text);
                        } catch (e) {
                            return onError(makeError('fromtexteval',
                                             'fromText eval for ' + id +
                                            ' failed: ' + e,
                                             e,
                                             [id]));
                        }

                        if (hasInteractive) {
                            useInteractive = true;
                        }

                        //Mark this as a dependency for the plugin
                        //resource
                        this.depMaps.push(moduleMap);

                        //Support anonymous modules.
                        context.completeLoad(moduleName);

                        //Bind the value of that module to the value for this
                        //resource ID.
                        localRequire([moduleName], load);
                    });

                    //Use parentName here since the plugin's name is not reliable,
                    //could be some weird string with no path that actually wants to
                    //reference the parentName's path.
                    plugin.load(map.name, localRequire, load, config);
                }));

                context.enable(pluginMap, this);
                this.pluginMaps[pluginMap.id] = pluginMap;
            },

            enable: function () {
                enabledRegistry[this.map.id] = this;
                this.enabled = true;

                //Set flag mentioning that the module is enabling,
                //so that immediate calls to the defined callbacks
                //for dependencies do not trigger inadvertent load
                //with the depCount still being zero.
                this.enabling = true;

                //Enable each dependency
                each(this.depMaps, bind(this, function (depMap, i) {
                    var id, mod, handler;

                    if (typeof depMap === 'string') {
                        //Dependency needs to be converted to a depMap
                        //and wired up to this module.
                        depMap = makeModuleMap(depMap,
                                               (this.map.isDefine ? this.map : this.map.parentMap),
                                               false,
                                               !this.skipMap);
                        this.depMaps[i] = depMap;

                        handler = getOwn(handlers, depMap.id);

                        if (handler) {
                            this.depExports[i] = handler(this);
                            return;
                        }

                        this.depCount += 1;

                        on(depMap, 'defined', bind(this, function (depExports) {
                            if (this.undefed) {
                                return;
                            }
                            this.defineDep(i, depExports);
                            this.check();
                        }));

                        if (this.errback) {
                            on(depMap, 'error', bind(this, this.errback));
                        } else if (this.events.error) {
                            // No direct errback on this module, but something
                            // else is listening for errors, so be sure to
                            // propagate the error correctly.
                            on(depMap, 'error', bind(this, function(err) {
                                this.emit('error', err);
                            }));
                        }
                    }

                    id = depMap.id;
                    mod = registry[id];

                    //Skip special modules like 'require', 'exports', 'module'
                    //Also, don't call enable if it is already enabled,
                    //important in circular dependency cases.
                    if (!hasProp(handlers, id) && mod && !mod.enabled) {
                        context.enable(depMap, this);
                    }
                }));

                //Enable each plugin that is used in
                //a dependency
                eachProp(this.pluginMaps, bind(this, function (pluginMap) {
                    var mod = getOwn(registry, pluginMap.id);
                    if (mod && !mod.enabled) {
                        context.enable(pluginMap, this);
                    }
                }));

                this.enabling = false;

                this.check();
            },

            on: function (name, cb) {
                var cbs = this.events[name];
                if (!cbs) {
                    cbs = this.events[name] = [];
                }
                cbs.push(cb);
            },

            emit: function (name, evt) {
                each(this.events[name], function (cb) {
                    cb(evt);
                });
                if (name === 'error') {
                    //Now that the error handler was triggered, remove
                    //the listeners, since this broken Module instance
                    //can stay around for a while in the registry.
                    delete this.events[name];
                }
            }
        };

        function callGetModule(args) {
            //Skip modules already defined.
            if (!hasProp(defined, args[0])) {
                getModule(makeModuleMap(args[0], null, true)).init(args[1], args[2]);
            }
        }

        function removeListener(node, func, name, ieName) {
            //Favor detachEvent because of IE9
            //issue, see attachEvent/addEventListener comment elsewhere
            //in this file.
            if (node.detachEvent && !isOpera) {
                //Probably IE. If not it will throw an error, which will be
                //useful to know.
                if (ieName) {
                    node.detachEvent(ieName, func);
                }
            } else {
                node.removeEventListener(name, func, false);
            }
        }

        /**
         * Given an event from a script node, get the requirejs info from it,
         * and then removes the event listeners on the node.
         * @param {Event} evt
         * @returns {Object}
         */
        function getScriptData(evt) {
            //Using currentTarget instead of target for Firefox 2.0's sake. Not
            //all old browsers will be supported, but this one was easy enough
            //to support and still makes sense.
            var node = evt.currentTarget || evt.srcElement;

            //Remove the listeners once here.
            removeListener(node, context.onScriptLoad, 'load', 'onreadystatechange');
            removeListener(node, context.onScriptError, 'error');

            return {
                node: node,
                id: node && node.getAttribute('data-requiremodule')
            };
        }

        function intakeDefines() {
            var args;

            //Any defined modules in the global queue, intake them now.
            takeGlobalQueue();

            //Make sure any remaining defQueue items get properly processed.
            while (defQueue.length) {
                args = defQueue.shift();
                if (args[0] === null) {
                    return onError(makeError('mismatch', 'Mismatched anonymous define() module: ' +
                        args[args.length - 1]));
                } else {
                    //args are id, deps, factory. Should be normalized by the
                    //define() function.
                    callGetModule(args);
                }
            }
            context.defQueueMap = {};
        }

        context = {
            config: config,
            contextName: contextName,
            registry: registry,
            defined: defined,
            urlFetched: urlFetched,
            defQueue: defQueue,
            defQueueMap: {},
            Module: Module,
            makeModuleMap: makeModuleMap,
            nextTick: req.nextTick,
            onError: onError,

            /**
             * Set a configuration for the context.
             * @param {Object} cfg config object to integrate.
             */
            configure: function (cfg) {
                //Make sure the baseUrl ends in a slash.
                if (cfg.baseUrl) {
                    if (cfg.baseUrl.charAt(cfg.baseUrl.length - 1) !== '/') {
                        cfg.baseUrl += '/';
                    }
                }

                //Save off the paths since they require special processing,
                //they are additive.
                var shim = config.shim,
                    objs = {
                        paths: true,
                        bundles: true,
                        config: true,
                        map: true
                    };

                eachProp(cfg, function (value, prop) {
                    if (objs[prop]) {
                        if (!config[prop]) {
                            config[prop] = {};
                        }
                        mixin(config[prop], value, true, true);
                    } else {
                        config[prop] = value;
                    }
                });

                //Reverse map the bundles
                if (cfg.bundles) {
                    eachProp(cfg.bundles, function (value, prop) {
                        each(value, function (v) {
                            if (v !== prop) {
                                bundlesMap[v] = prop;
                            }
                        });
                    });
                }

                //Merge shim
                if (cfg.shim) {
                    eachProp(cfg.shim, function (value, id) {
                        //Normalize the structure
                        if (isArray(value)) {
                            value = {
                                deps: value
                            };
                        }
                        if ((value.exports || value.init) && !value.exportsFn) {
                            value.exportsFn = context.makeShimExports(value);
                        }
                        shim[id] = value;
                    });
                    config.shim = shim;
                }

                //Adjust packages if necessary.
                if (cfg.packages) {
                    each(cfg.packages, function (pkgObj) {
                        var location, name;

                        pkgObj = typeof pkgObj === 'string' ? {name: pkgObj} : pkgObj;

                        name = pkgObj.name;
                        location = pkgObj.location;
                        if (location) {
                            config.paths[name] = pkgObj.location;
                        }

                        //Save pointer to main module ID for pkg name.
                        //Remove leading dot in main, so main paths are normalized,
                        //and remove any trailing .js, since different package
                        //envs have different conventions: some use a module name,
                        //some use a file name.
                        config.pkgs[name] = pkgObj.name + '/' + (pkgObj.main || 'main')
                                     .replace(currDirRegExp, '')
                                     .replace(jsSuffixRegExp, '');
                    });
                }

                //If there are any "waiting to execute" modules in the registry,
                //update the maps for them, since their info, like URLs to load,
                //may have changed.
                eachProp(registry, function (mod, id) {
                    //If module already has init called, since it is too
                    //late to modify them, and ignore unnormalized ones
                    //since they are transient.
                    if (!mod.inited && !mod.map.unnormalized) {
                        mod.map = makeModuleMap(id, null, true);
                    }
                });

                //If a deps array or a config callback is specified, then call
                //require with those args. This is useful when require is defined as a
                //config object before require.js is loaded.
                if (cfg.deps || cfg.callback) {
                    context.require(cfg.deps || [], cfg.callback);
                }
            },

            makeShimExports: function (value) {
                function fn() {
                    var ret;
                    if (value.init) {
                        ret = value.init.apply(global, arguments);
                    }
                    return ret || (value.exports && getGlobal(value.exports));
                }
                return fn;
            },

            makeRequire: function (relMap, options) {
                options = options || {};

                function localRequire(deps, callback, errback) {
                    var id, map, requireMod;

                    if (options.enableBuildCallback && callback && isFunction(callback)) {
                        callback.__requireJsBuild = true;
                    }

                    if (typeof deps === 'string') {
                        if (isFunction(callback)) {
                            //Invalid call
                            return onError(makeError('requireargs', 'Invalid require call'), errback);
                        }

                        //If require|exports|module are requested, get the
                        //value for them from the special handlers. Caveat:
                        //this only works while module is being defined.
                        if (relMap && hasProp(handlers, deps)) {
                            return handlers[deps](registry[relMap.id]);
                        }

                        //Synchronous access to one module. If require.get is
                        //available (as in the Node adapter), prefer that.
                        if (req.get) {
                            return req.get(context, deps, relMap, localRequire);
                        }

                        //Normalize module name, if it contains . or ..
                        map = makeModuleMap(deps, relMap, false, true);
                        id = map.id;

                        if (!hasProp(defined, id)) {
                            return onError(makeError('notloaded', 'Module name "' +
                                        id +
                                        '" has not been loaded yet for context: ' +
                                        contextName +
                                        (relMap ? '' : '. Use require([])')));
                        }
                        return defined[id];
                    }

                    //Grab defines waiting in the global queue.
                    intakeDefines();

                    //Mark all the dependencies as needing to be loaded.
                    context.nextTick(function () {
                        //Some defines could have been added since the
                        //require call, collect them.
                        intakeDefines();

                        requireMod = getModule(makeModuleMap(null, relMap));

                        //Store if map config should be applied to this require
                        //call for dependencies.
                        requireMod.skipMap = options.skipMap;

                        requireMod.init(deps, callback, errback, {
                            enabled: true
                        });

                        checkLoaded();
                    });

                    return localRequire;
                }

                mixin(localRequire, {
                    isBrowser: isBrowser,

                    /**
                     * Converts a module name + .extension into an URL path.
                     * *Requires* the use of a module name. It does not support using
                     * plain URLs like nameToUrl.
                     */
                    toUrl: function (moduleNamePlusExt) {
                        var ext,
                            index = moduleNamePlusExt.lastIndexOf('.'),
                            segment = moduleNamePlusExt.split('/')[0],
                            isRelative = segment === '.' || segment === '..';

                        //Have a file extension alias, and it is not the
                        //dots from a relative path.
                        if (index !== -1 && (!isRelative || index > 1)) {
                            ext = moduleNamePlusExt.substring(index, moduleNamePlusExt.length);
                            moduleNamePlusExt = moduleNamePlusExt.substring(0, index);
                        }

                        return context.nameToUrl(normalize(moduleNamePlusExt,
                                                relMap && relMap.id, true), ext,  true);
                    },

                    defined: function (id) {
                        return hasProp(defined, makeModuleMap(id, relMap, false, true).id);
                    },

                    specified: function (id) {
                        id = makeModuleMap(id, relMap, false, true).id;
                        return hasProp(defined, id) || hasProp(registry, id);
                    }
                });

                //Only allow undef on top level require calls
                if (!relMap) {
                    localRequire.undef = function (id) {
                        //Bind any waiting define() calls to this context,
                        //fix for #408
                        takeGlobalQueue();

                        var map = makeModuleMap(id, relMap, true),
                            mod = getOwn(registry, id);

                        mod.undefed = true;
                        removeScript(id);

                        delete defined[id];
                        delete urlFetched[map.url];
                        delete undefEvents[id];

                        //Clean queued defines too. Go backwards
                        //in array so that the splices do not
                        //mess up the iteration.
                        eachReverse(defQueue, function(args, i) {
                            if (args[0] === id) {
                                defQueue.splice(i, 1);
                            }
                        });
                        delete context.defQueueMap[id];

                        if (mod) {
                            //Hold on to listeners in case the
                            //module will be attempted to be reloaded
                            //using a different config.
                            if (mod.events.defined) {
                                undefEvents[id] = mod.events;
                            }

                            cleanRegistry(id);
                        }
                    };
                }

                return localRequire;
            },

            /**
             * Called to enable a module if it is still in the registry
             * awaiting enablement. A second arg, parent, the parent module,
             * is passed in for context, when this method is overridden by
             * the optimizer. Not shown here to keep code compact.
             */
            enable: function (depMap) {
                var mod = getOwn(registry, depMap.id);
                if (mod) {
                    getModule(depMap).enable();
                }
            },

            /**
             * Internal method used by environment adapters to complete a load event.
             * A load event could be a script load or just a load pass from a synchronous
             * load call.
             * @param {String} moduleName the name of the module to potentially complete.
             */
            completeLoad: function (moduleName) {
                var found, args, mod,
                    shim = getOwn(config.shim, moduleName) || {},
                    shExports = shim.exports;

                takeGlobalQueue();

                while (defQueue.length) {
                    args = defQueue.shift();
                    if (args[0] === null) {
                        args[0] = moduleName;
                        //If already found an anonymous module and bound it
                        //to this name, then this is some other anon module
                        //waiting for its completeLoad to fire.
                        if (found) {
                            break;
                        }
                        found = true;
                    } else if (args[0] === moduleName) {
                        //Found matching define call for this script!
                        found = true;
                    }

                    callGetModule(args);
                }
                context.defQueueMap = {};

                //Do this after the cycle of callGetModule in case the result
                //of those calls/init calls changes the registry.
                mod = getOwn(registry, moduleName);

                if (!found && !hasProp(defined, moduleName) && mod && !mod.inited) {
                    if (config.enforceDefine && (!shExports || !getGlobal(shExports))) {
                        if (hasPathFallback(moduleName)) {
                            return;
                        } else {
                            return onError(makeError('nodefine',
                                             'No define call for ' + moduleName,
                                             null,
                                             [moduleName]));
                        }
                    } else {
                        //A script that does not call define(), so just simulate
                        //the call for it.
                        callGetModule([moduleName, (shim.deps || []), shim.exportsFn]);
                    }
                }

                checkLoaded();
            },

            /**
             * Converts a module name to a file path. Supports cases where
             * moduleName may actually be just an URL.
             * Note that it **does not** call normalize on the moduleName,
             * it is assumed to have already been normalized. This is an
             * internal API, not a public one. Use toUrl for the public API.
             */
            nameToUrl: function (moduleName, ext, skipExt) {
                var paths, syms, i, parentModule, url,
                    parentPath, bundleId,
                    pkgMain = getOwn(config.pkgs, moduleName);

                if (pkgMain) {
                    moduleName = pkgMain;
                }

                bundleId = getOwn(bundlesMap, moduleName);

                if (bundleId) {
                    return context.nameToUrl(bundleId, ext, skipExt);
                }

                //If a colon is in the URL, it indicates a protocol is used and it is just
                //an URL to a file, or if it starts with a slash, contains a query arg (i.e. ?)
                //or ends with .js, then assume the user meant to use an url and not a module id.
                //The slash is important for protocol-less URLs as well as full paths.
                if (req.jsExtRegExp.test(moduleName)) {
                    //Just a plain path, not module name lookup, so just return it.
                    //Add extension if it is included. This is a bit wonky, only non-.js things pass
                    //an extension, this method probably needs to be reworked.
                    url = moduleName + (ext || '');
                } else {
                    //A module that needs to be converted to a path.
                    paths = config.paths;

                    syms = moduleName.split('/');
                    //For each module name segment, see if there is a path
                    //registered for it. Start with most specific name
                    //and work up from it.
                    for (i = syms.length; i > 0; i -= 1) {
                        parentModule = syms.slice(0, i).join('/');

                        parentPath = getOwn(paths, parentModule);
                        if (parentPath) {
                            //If an array, it means there are a few choices,
                            //Choose the one that is desired
                            if (isArray(parentPath)) {
                                parentPath = parentPath[0];
                            }
                            syms.splice(0, i, parentPath);
                            break;
                        }
                    }

                    //Join the path parts together, then figure out if baseUrl is needed.
                    url = syms.join('/');
                    url += (ext || (/^data\:|\?/.test(url) || skipExt ? '' : '.js'));
                    url = (url.charAt(0) === '/' || url.match(/^[\w\+\.\-]+:/) ? '' : config.baseUrl) + url;
                }

                return config.urlArgs ? url +
                                        ((url.indexOf('?') === -1 ? '?' : '&') +
                                         config.urlArgs) : url;
            },

            //Delegates to req.load. Broken out as a separate function to
            //allow overriding in the optimizer.
            load: function (id, url) {
                req.load(context, id, url);
            },

            /**
             * Executes a module callback function. Broken out as a separate function
             * solely to allow the build system to sequence the files in the built
             * layer in the right sequence.
             *
             * @private
             */
            execCb: function (name, callback, args, exports) {
                return callback.apply(exports, args);
            },

            /**
             * callback for script loads, used to check status of loading.
             *
             * @param {Event} evt the event from the browser for the script
             * that was loaded.
             */
            onScriptLoad: function (evt) {
                //Using currentTarget instead of target for Firefox 2.0's sake. Not
                //all old browsers will be supported, but this one was easy enough
                //to support and still makes sense.
                if (evt.type === 'load' ||
                        (readyRegExp.test((evt.currentTarget || evt.srcElement).readyState))) {
                    //Reset interactive script so a script node is not held onto for
                    //to long.
                    interactiveScript = null;

                    //Pull out the name of the module and the context.
                    var data = getScriptData(evt);
                    context.completeLoad(data.id);
                }
            },

            /**
             * Callback for script errors.
             */
            onScriptError: function (evt) {
                var data = getScriptData(evt);
                if (!hasPathFallback(data.id)) {
                    var parents = [];
                    eachProp(registry, function(value, key) {
                        if (key.indexOf('_@r') !== 0) {
                            each(value.depMaps, function(depMap) {
                                if (depMap.id === data.id) {
                                    parents.push(key);
                                }
                                return true;
                            });
                        }
                    });
                    return onError(makeError('scripterror', 'Script error for "' + data.id +
                                             (parents.length ?
                                             '", needed by: ' + parents.join(', ') :
                                             '"'), evt, [data.id]));
                }
            }
        };

        context.require = context.makeRequire();
        return context;
    }

    /**
     * Main entry point.
     *
     * If the only argument to require is a string, then the module that
     * is represented by that string is fetched for the appropriate context.
     *
     * If the first argument is an array, then it will be treated as an array
     * of dependency string names to fetch. An optional function callback can
     * be specified to execute when all of those dependencies are available.
     *
     * Make a local req variable to help Caja compliance (it assumes things
     * on a require that are not standardized), and to give a short
     * name for minification/local scope use.
     */
    req = requirejs = function (deps, callback, errback, optional) {

        //Find the right context, use default
        var context, config,
            contextName = defContextName;

        // Determine if have config object in the call.
        if (!isArray(deps) && typeof deps !== 'string') {
            // deps is a config object
            config = deps;
            if (isArray(callback)) {
                // Adjust args if there are dependencies
                deps = callback;
                callback = errback;
                errback = optional;
            } else {
                deps = [];
            }
        }

        if (config && config.context) {
            contextName = config.context;
        }

        context = getOwn(contexts, contextName);
        if (!context) {
            context = contexts[contextName] = req.s.newContext(contextName);
        }

        if (config) {
            context.configure(config);
        }

        return context.require(deps, callback, errback);
    };

    /**
     * Support require.config() to make it easier to cooperate with other
     * AMD loaders on globally agreed names.
     */
    req.config = function (config) {
        return req(config);
    };

    /**
     * Execute something after the current tick
     * of the event loop. Override for other envs
     * that have a better solution than setTimeout.
     * @param  {Function} fn function to execute later.
     */
    req.nextTick = typeof setTimeout !== 'undefined' ? function (fn) {
        setTimeout(fn, 4);
    } : function (fn) { fn(); };

    /**
     * Export require as a global, but only if it does not already exist.
     */
    if (!require) {
        require = req;
    }

    req.version = version;

    //Used to filter out dependencies that are already paths.
    req.jsExtRegExp = /^\/|:|\?|\.js$/;
    req.isBrowser = isBrowser;
    s = req.s = {
        contexts: contexts,
        newContext: newContext
    };

    //Create default context.
    req({});

    //Exports some context-sensitive methods on global require.
    each([
        'toUrl',
        'undef',
        'defined',
        'specified'
    ], function (prop) {
        //Reference from contexts instead of early binding to default context,
        //so that during builds, the latest instance of the default context
        //with its config gets used.
        req[prop] = function () {
            var ctx = contexts[defContextName];
            return ctx.require[prop].apply(ctx, arguments);
        };
    });

    if (isBrowser) {
        head = s.head = document.getElementsByTagName('head')[0];
        //If BASE tag is in play, using appendChild is a problem for IE6.
        //When that browser dies, this can be removed. Details in this jQuery bug:
        //http://dev.jquery.com/ticket/2709
        baseElement = document.getElementsByTagName('base')[0];
        if (baseElement) {
            head = s.head = baseElement.parentNode;
        }
    }

    /**
     * Any errors that require explicitly generates will be passed to this
     * function. Intercept/override it if you want custom error handling.
     * @param {Error} err the error object.
     */
    req.onError = defaultOnError;

    /**
     * Creates the node for the load command. Only used in browser envs.
     */
    req.createNode = function (config, moduleName, url) {
        var node = config.xhtml ?
                document.createElementNS('http://www.w3.org/1999/xhtml', 'html:script') :
                document.createElement('script');
        node.type = config.scriptType || 'text/javascript';
        node.charset = 'utf-8';
        node.async = true;
        return node;
    };

    /**
     * Does the request to load a module for the browser case.
     * Make this a separate function to allow other environments
     * to override it.
     *
     * @param {Object} context the require context to find state.
     * @param {String} moduleName the name of the module.
     * @param {Object} url the URL to the module.
     */
    req.load = function (context, moduleName, url) {
        var config = (context && context.config) || {},
            node;
        if (isBrowser) {
            //In the browser so use a script tag
            node = req.createNode(config, moduleName, url);
            if (config.onNodeCreated) {
                config.onNodeCreated(node, config, moduleName, url);
            }

            node.setAttribute('data-requirecontext', context.contextName);
            node.setAttribute('data-requiremodule', moduleName);

            //Set up load listener. Test attachEvent first because IE9 has
            //a subtle issue in its addEventListener and script onload firings
            //that do not match the behavior of all other browsers with
            //addEventListener support, which fire the onload event for a
            //script right after the script execution. See:
            //https://connect.microsoft.com/IE/feedback/details/648057/script-onload-event-is-not-fired-immediately-after-script-execution
            //UNFORTUNATELY Opera implements attachEvent but does not follow the script
            //script execution mode.
            if (node.attachEvent &&
                    //Check if node.attachEvent is artificially added by custom script or
                    //natively supported by browser
                    //read https://github.com/jrburke/requirejs/issues/187
                    //if we can NOT find [native code] then it must NOT natively supported.
                    //in IE8, node.attachEvent does not have toString()
                    //Note the test for "[native code" with no closing brace, see:
                    //https://github.com/jrburke/requirejs/issues/273
                    !(node.attachEvent.toString && node.attachEvent.toString().indexOf('[native code') < 0) &&
                    !isOpera) {
                //Probably IE. IE (at least 6-8) do not fire
                //script onload right after executing the script, so
                //we cannot tie the anonymous define call to a name.
                //However, IE reports the script as being in 'interactive'
                //readyState at the time of the define call.
                useInteractive = true;

                node.attachEvent('onreadystatechange', context.onScriptLoad);
                //It would be great to add an error handler here to catch
                //404s in IE9+. However, onreadystatechange will fire before
                //the error handler, so that does not help. If addEventListener
                //is used, then IE will fire error before load, but we cannot
                //use that pathway given the connect.microsoft.com issue
                //mentioned above about not doing the 'script execute,
                //then fire the script load event listener before execute
                //next script' that other browsers do.
                //Best hope: IE10 fixes the issues,
                //and then destroys all installs of IE 6-9.
                //node.attachEvent('onerror', context.onScriptError);
            } else {
                node.addEventListener('load', context.onScriptLoad, false);
                node.addEventListener('error', context.onScriptError, false);
            }
            node.src = url;

            //For some cache cases in IE 6-8, the script executes before the end
            //of the appendChild execution, so to tie an anonymous define
            //call to the module name (which is stored on the node), hold on
            //to a reference to this node, but clear after the DOM insertion.
            currentlyAddingScript = node;
            if (baseElement) {
                head.insertBefore(node, baseElement);
            } else {
                head.appendChild(node);
            }
            currentlyAddingScript = null;

            return node;
        } else if (isWebWorker) {
            try {
                //In a web worker, use importScripts. This is not a very
                //efficient use of importScripts, importScripts will block until
                //its script is downloaded and evaluated. However, if web workers
                //are in play, the expectation is that a build has been done so
                //that only one script needs to be loaded anyway. This may need
                //to be reevaluated if other use cases become common.
                importScripts(url);

                //Account for anonymous modules
                context.completeLoad(moduleName);
            } catch (e) {
                context.onError(makeError('importscripts',
                                'importScripts failed for ' +
                                    moduleName + ' at ' + url,
                                e,
                                [moduleName]));
            }
        }
    };

    function getInteractiveScript() {
        if (interactiveScript && interactiveScript.readyState === 'interactive') {
            return interactiveScript;
        }

        eachReverse(scripts(), function (script) {
            if (script.readyState === 'interactive') {
                return (interactiveScript = script);
            }
        });
        return interactiveScript;
    }

    //Look for a data-main script attribute, which could also adjust the baseUrl.
    if (isBrowser && !cfg.skipDataMain) {
        //Figure out baseUrl. Get it from the script tag with require.js in it.
        eachReverse(scripts(), function (script) {
            //Set the 'head' where we can append children by
            //using the script's parent.
            if (!head) {
                head = script.parentNode;
            }

            //Look for a data-main attribute to set main script for the page
            //to load. If it is there, the path to data main becomes the
            //baseUrl, if it is not already set.
            dataMain = script.getAttribute('data-main');
            if (dataMain) {
                //Preserve dataMain in case it is a path (i.e. contains '?')
                mainScript = dataMain;

                //Set final baseUrl if there is not already an explicit one.
                if (!cfg.baseUrl) {
                    //Pull off the directory of data-main for use as the
                    //baseUrl.
                    src = mainScript.split('/');
                    mainScript = src.pop();
                    subPath = src.length ? src.join('/')  + '/' : './';

                    cfg.baseUrl = subPath;
                }

                //Strip off any trailing .js since mainScript is now
                //like a module name.
                mainScript = mainScript.replace(jsSuffixRegExp, '');

                //If mainScript is still a path, fall back to dataMain
                if (req.jsExtRegExp.test(mainScript)) {
                    mainScript = dataMain;
                }

                //Put the data-main script in the files to load.
                cfg.deps = cfg.deps ? cfg.deps.concat(mainScript) : [mainScript];

                return true;
            }
        });
    }

    /**
     * The function that handles definitions of modules. Differs from
     * require() in that a string for the module should be the first argument,
     * and the function to execute after dependencies are loaded should
     * return a value to define the module corresponding to the first argument's
     * name.
     */
    define = function (name, deps, callback) {
        var node, context;

        //Allow for anonymous modules
        if (typeof name !== 'string') {
            //Adjust args appropriately
            callback = deps;
            deps = name;
            name = null;
        }

        //This module may not have dependencies
        if (!isArray(deps)) {
            callback = deps;
            deps = null;
        }

        //If no name, and callback is a function, then figure out if it a
        //CommonJS thing with dependencies.
        if (!deps && isFunction(callback)) {
            deps = [];
            //Remove comments from the callback string,
            //look for require calls, and pull them into the dependencies,
            //but only if there are function args.
            if (callback.length) {
                callback
                    .toString()
                    .replace(commentRegExp, '')
                    .replace(cjsRequireRegExp, function (match, dep) {
                        deps.push(dep);
                    });

                //May be a CommonJS thing even without require calls, but still
                //could use exports, and module. Avoid doing exports and module
                //work though if it just needs require.
                //REQUIRES the function to expect the CommonJS variables in the
                //order listed below.
                deps = (callback.length === 1 ? ['require'] : ['require', 'exports', 'module']).concat(deps);
            }
        }

        //If in IE 6-8 and hit an anonymous define() call, do the interactive
        //work.
        if (useInteractive) {
            node = currentlyAddingScript || getInteractiveScript();
            if (node) {
                if (!name) {
                    name = node.getAttribute('data-requiremodule');
                }
                context = contexts[node.getAttribute('data-requirecontext')];
            }
        }

        //Always save off evaluating the def call until the script onload handler.
        //This allows multiple modules to be in a file without prematurely
        //tracing dependencies, and allows for anonymous module support,
        //where the module name is not known until the script onload event
        //occurs. If no context, use the global queue, and get it processed
        //in the onscript load callback.
        if (context) {
            context.defQueue.push([name, deps, callback]);
            context.defQueueMap[name] = true;
        } else {
            globalDefQueue.push([name, deps, callback]);
        }
    };

    define.amd = {
        jQuery: true
    };

    /**
     * Executes the text. Normally just uses eval, but can be modified
     * to use a better, environment-specific call. Only used for transpiling
     * loader plugins, not for plain JS modules.
     * @param {String} text the text to execute/evaluate.
     */
    req.exec = function (text) {
        /*jslint evil: true */
        return eval(text);
    };

    //Set up with config info.
    req(cfg);
}(this));
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"## 1) Perform further data exploration on the HADS national dataset (the version before we one-hot encoded it) Make scatterplots and see if you can see any resemblance between the original scatterplots and the plot of the principal components that you made in 7.1. \n", + "\n", + "(You may or may not not see very much resemblance depending on the variables you choose, and that's ok!)\n", + "\n", + "## 2) Study \"Scree Plots\" and then try and make one for your PCA dataset. How many principal conponents do you need to retain in order for your PCs to contain 90% of the explained variance? \n", + "\n", + "We will present this topic formally at the beginning of tomorrow's lecture, so if you figure this stretch goal out, you're ahead of the game. \n", + "\n", + "## 3) Explore further the intuition behind eigenvalues and eigenvectors by creating your very own eigenfaces:\n", + "\n", + "Prioritize self-study over this stretch goal if you are not semi-comfortable with the topics of PCA, Eigenvalues, and Eigenvectors.\n", + "\n", + "![Eigenfaces](https://i.pinimg.com/236x/1c/f1/01/1cf101a9859437a5d096a04b05be06b4--faces-tattoo.jpg)\n", + "\n", + "You don't necessarily have to use this resource, but this will get you started: \n", + "[Eigenface Tutorial](https://sandipanweb.wordpress.com/2018/01/06/eigenfaces-and-a-simple-face-detector-with-pca-svd-in-python/)" + ] + } + ] +} \ No newline at end of file diff --git a/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb b/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb index 87fc432d..15ba2100 100644 --- a/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb +++ b/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb @@ -43,11 +43,66 @@ "colab": {} }, "source": [ - "" + "import numpy as np \n", + "import matplotlib.pyplot as plt \n", + "import math" ], - "execution_count": 0, + "execution_count": 4, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "CaMSSLaot5_k", + "colab_type": "code", + "colab": {} + }, + "source": [ + "vector_two = [4,5]" + ], + "execution_count": 9, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "nhs7eMrzuIZq", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 269 + }, + "outputId": "be12151d-4a6e-4c72-a506-784869a312ef" + }, + "source": [ + "fig, ax = plt.subplots()\n", + "ax.grid()\n", + "plt.xlim(0,6)\n", + "plt.ylim(0,6)\n", + "plt.arrow(0,0,\n", + " vector_two[0], vector_two[1], \n", + " head_width=.2, \n", + " linewidth = 2, \n", + " color = 'b')\n", + "plt.show();" + ], + "execution_count": 10, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -58,6 +113,19 @@ "## 1.2 Create a three-dimensional vecor and plot it on a graph" ] }, + { + "cell_type": "code", + "metadata": { + "id": "i1vQ2DVnvhzD", + "colab_type": "code", + "colab": {} + }, + "source": [ + "from mpl_toolkits.mplot3d import Axes3D" + ], + "execution_count": 11, + "outputs": [] + }, { "cell_type": "code", "metadata": { @@ -66,11 +134,53 @@ "colab": {} }, "source": [ - "" + "vector_three = [2,4,1]" ], - "execution_count": 0, + "execution_count": 12, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "Xf7rW04mvpsi", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 248 + }, + "outputId": "d73d2232-1e07-491d-afd2-dc452993c787" + }, + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_subplot(111, projection= '3d')\n", + "ax.quiver(0,0,0,vector_three[0], vector_three[1], vector_three[2], length=1, color='b')\n", + "\n", + "ax.set_xlim([0,5])\n", + "ax.set_ylim([0,5])\n", + "ax.set_zlim([0,5])\n", + "ax.set_xlabel('X')\n", + "ax.set_ylabel('Y')\n", + "ax.set_zlabel('Z')\n", + "\n", + "plt.show();" + ], + "execution_count": 17, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -86,18 +196,18 @@ "metadata": { "id": "ah6zMSLJdJwL", "colab_type": "code", - "outputId": "b1ccb836-02b8-4d42-a7db-6c34f010f6c6", "colab": { "base_uri": "https://localhost:8080/", - "height": 52 - } + "height": 51 + }, + "outputId": "103c415f-4847-4ff1-9df3-617a0b3a5913" }, "source": [ "from math import e, pi\n", "print(e)\n", "print(pi)" ], - "execution_count": 0, + "execution_count": 19, "outputs": [ { "output_type": "stream", @@ -117,11 +227,56 @@ "colab": {} }, "source": [ - "" + "original = vector_two\n", + "scaled_by_e = np.multiply(e, vector_two)\n", + "scaled_by_pi = np.multiply(pi, vector_two)" ], - "execution_count": 0, + "execution_count": 20, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "B4pT4rv9xlXq", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 269 + }, + "outputId": "99be9128-08f0-45d3-ab03-148b52d8c2d3" + }, + "source": [ + "fig, ax = plt.subplots()\n", + "ax.grid()\n", + "plt.xlim([0,20])\n", + "plt.ylim([0,20])\n", + "\n", + "for color, vector in [('green', scaled_by_pi), ('blue', scaled_by_e), ('red', original)]:\n", + " plt.arrow(0,0,\n", + " vector[0], vector[1],\n", + " head_width = .5, \n", + " head_length= .5,\n", + " linewidth = 2, \n", + " color = color)\n", + "plt.show();" + ], + "execution_count": 30, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -146,11 +301,54 @@ "colab": {} }, "source": [ - "" + "a = [5,7]\n", + "b = [3,4]" ], - "execution_count": 0, + "execution_count": 31, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "IsfCP9lMzmtX", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 269 + }, + "outputId": "db03c8e0-89f0-4b06-d64a-0da6898da023" + }, + "source": [ + "fig, ax = plt.subplots()\n", + "ax.grid()\n", + "plt.xlim(0,10)\n", + "plt.ylim(0,10)\n", + "for color, vector in [('green', a), ('blue', b)]:\n", + " plt.arrow(0, 0,\n", + " vector[0], vector[1],\n", + " head_width = .2,\n", + " head_length = .2, \n", + " linewidth = 2,\n", + " color = color)\n", + "plt.show();" + ], + "execution_count": 38, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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WHRs1CsaPD1SYiMSK5twbUY1Vp5tbw4NvR8defRVOPz1QYSISOwr3RuDudBzdkVVVqxIdr46G87pExxcsgG7dwtQmIvGkcG9gtb/rdL8HP2Dbiu/BeeUAbNwIBx20l4tFRNKkcG9AW7ZvoeXtLRON5OZf23Y7rs2/RKSh6APVBrJ209pUsG85GIbvjI716QM9eyrYRaThKNwbQI3vOl1bDCM2RMduuAGmTQtUmIgUDE3LZNmM5TPo81CfRGNBf3ji5ejYE0/ARRcFKkxECorCPYuemfMM5z19XqLx1jD4+4jo2KxZiakYEZHGoHDPkrtn3M1/vfZficZTE2HeOdGxlSvh0EMDFSYiBUnhngXXvXwd975zLzjwu89h24HRsa1boXnzvV8rItIQFO4ZOu2vp/H3xX+H7S3gti1Rf6dOsHy59ogRkTB0t0ya3J2Oozomgv3zTjWC/eKLYcUKBbuIhKN37mmosep0+Ynw5xnRsTFjYPDgQIWJiCQp3OupxqrT9y6D5x6Ojk2aBP36halLRGR3aYe7mR0GPAq0J/FR4jh3H5OtwnJR5eZK2t7VNtF46Q/wzrXRsUWL4IgjAhUmIlJLJu/cdwC/cPd3zezbQIWZTXL3OVmqLafU+K7TB96H1cdFx774Ar797UCFiYjsQdrh7u4rgZXJn780s7lAJyB24R6tOt3ZFG7dUePYzp3QRB9Li0iOMXfP/EHMugBvAse6+xe1jg0CBgG0bdu2Z1lZWcbP15g2bt2Y+Eq86qaw6p+i/qIiKC5O/3GrqqooKirKQoX5T2ORorFI0ViklJaWVrh7r3pd5O4Z/QKKgArgx/s6t3v37p5P7p5xt/MbnGuOdvDo1003Zf7YU6ZMyfxBYkJjkaKxSNFYpACzvJ7ZnNHdMmb2LeAZ4HF3n5jJY+WaaNXpvB/CU89H/ePHJ77EWkQkl2Vyt4wBfwbmuvvo7JUU3r/+9V+ZtHgSvPkrmHxb1P/uu3D88QELExGpo0zeuZ8E/BvwoZm9n+z7lbu//A3X5DR3p/Pdnfnsy8/g8Rdg4VnRsdWroV27gMWJiNRDJnfLvAXEZoF9tOrUgds2wY6W0bGvvoL99gtXm4hIfekmPhKrTpvd2gy27Q+/9SjYu3aF6moFu4jkn4IP98rNlYntBDYeBrdvjvovvRQWL9bmXyKSnwo63BetX5TYTuCTk+CeZVH/fffBI4+Eq0tEJFMFu3HYzBUz6f3n3lBxObzwp6h/yhQoKQlXl4hINhRkuE+cO5Fzy86FF8ZCxZVR/+LFiXl2EZF8V3Dhfs/Me7j+/66He+dA5dFR/5dfJrYUEBGJg4IK98GvDOYPMx6AW1P76ZjBjh3a/EtE4qVgIu30x07nD1OegFu3R339+iVudVSwi0jcxD7W3J1Oozvx2vTP4K7KqP/mmxPfnCQiEkexnpap9mqaDm8Kc38E45+N+idMgHPPDViYiEgDi224R991Wn4zlP826v/gA/je9wIWJiLSCGIZ7tF3nf71Ffj4jKh/7Vpo0yZgYSIijSR24b5o/SK6jeme+ODUU/9527bBt74VsDARkUYUqw9UZ66YSbdRx8Hw6ijYu3dP3BGjYBeRQhKbcH927rP0Hnkh3L4p6rv8cpg/X5t/iUjhicW0zJiZY/jPP06ER5ZGfWPHwpVX7v0aEZE4y/twH/LKEH5/3zZ46Y2o7403oG/fgEWJiASW1+F++mOn89ro8+G9n0V9S5fCd74TriYRkVyQl+GeWHXamZW3vQEbjoz6q6rggAMCFiYikiPyLtyrvZqmN7eA/90W9TVv7mzZYvrgVEQkKa/ultmyfQtNb2xfI9j794etWxXsIiK7y5twr9xcScvBJ8Jda6O+4cPh5ZcDFiUikqPyYlrm4/Ufc+RVN8LTH0R9f/sbDBwYsCgRkRyW8+E+c8VMel88Cd6cEPV9+CEce2zAokREclxOh/uzc5/lx2ceBEt/HfVVVkLr1gGLEhHJAzkb7vfM+D3X9xlco2/7dmiWsxWLiOSOnPxA9epnhtUI9qOO3oG7gl1EpK5yLtz7jr6MsefdGbWvuHIHc+co1UVE6iNnUtPdaXfNBVSOLYv6xv2pmisuz5kSRUTyRk4kZ7VX03TAYHglFexTpzonn5xz/7AQEckLwcN9y/YttOz1NPy/e6O+ZcvgsMO05FREJF1Bw33tpkraddwMX/x71LdpE7RsGbAoEZEYCDbvMXfVx7QragNfHA5A85ZfUV2tYBcRyYYg4f7yexUc0+GIqP390pVs3dRcm3+JiGRJo4f7qGemMKBHz6h91Y3L+MfkDo1dhohIrGUU7mZ2hpnNN7NFZvbLfZ2/bftOhp5XGrXHPfkZD9xxeCYliIjIHqT9gaqZNQXuA04DVgDvmNnz7j5nb9fs2N40+nlaxQb69OiY7tOLiMg3yORumROARe6+GMDMngIGAnsN910+Xb2Fju0OyeCpRUTkm2QS7p2A5bu1VwD/XPskMxsEDEo2vwKb3al9Bs8aH22AytBF5AiNRYrGIkVjkVJc3wsa/D53dx8HjAMws1nu3quhnzMfaCxSNBYpGosUjUWKmc2q7zWZfKD6KXDYbu3OyT4REQksk3B/B+hmZl3NbD/gQuD57JQlIiKZSHtaxt13mNm1wP8BTYGH3P2jfVw2Lt3niyGNRYrGIkVjkaKxSKn3WJi7N0QhIiISkPbUFRGJIYW7iEgMNUq413ebgrgys8PMbIqZzTGzj8xsSOiaQjOzpmb2npm9GLqWkMzsYDObYGbzzGyumfUOXVMoZnZ98vUx28yeNLMWoWtqLGb2kJmtMbPZu/W1MrNJZrYw+XudVoA2eLjvtk1Bf+AY4CIzO6ahnzdH7QB+4e7HACcCPy/gsdhlCDA3dBE5YAzwqrsfBRxHgY6JmXUCBgO93P1YEjdrXBi2qkb1CHBGrb5fAq+7ezfg9WR7nxrjnXu0TYG7bwN2bVNQcNx9pbu/m/z5SxIv4E5hqwrHzDoDA4AHQ9cSkpkdBPQF/gzg7tvcfWPYqoJqBuxvZs2AlsBngetpNO7+JrC+VvdA4C/Jn/8C/Kguj9UY4b6nbQoKNtB2MbMuwPHA22ErCeoeYBhQHbqQwLoCa4GHk1NUD5rZAaGLCsHdPwVGAsuAlcDn7v5a2KqCa+/uK5M/rwLqtIGLPlANwMyKgGeA/3T3L0LXE4KZnQWscfeK0LXkgGZAD+ABdz8e2EQd/+kdN8n55IEk/sLrCBxgZpeErSp3eOLe9Trdv94Y4a5tCnZjZt8iEeyPu/vE0PUEdBJwtpktJTFV9wMzeyxsScGsAFa4+65/xU0gEfaFqB+wxN3Xuvt2YCLQJ3BNoa02sw4Ayd/X1OWixgh3bVOQZGZGYl51rruPDl1PSO5+k7t3dvcuJP5MTHb3gnyH5u6rgOVmtmvnv1Opw9bZMbUMONHMWiZfL6dSoB8u7+Z54NLkz5cCz9XlosbYFTKdbQri6iTg34APzez9ZN+v3P3lgDVJbrgOeDz5Bmgx8NPA9QTh7m+b2QTgXRJ3l71HAW1DYGZPAiVAGzNbAdwC3AGUmdnPgE+A8+v0WNp+QEQkfvSBqohIDCncRURiSOEuIhJDCncRkRhSuIuIxJDCXUQkhhTuIiIx9P8Bb48bCjEY/0YAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -169,11 +367,62 @@ "colab": {} }, "source": [ - "" + "a_b = np.array(a) - np.array(b)" ], - "execution_count": 0, + "execution_count": 39, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "GFfES9kL03EJ", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 269 + }, + "outputId": "2e2be39b-2cd9-4256-dbf4-fa81eef24911" + }, + "source": [ + "fig, ax = plt.subplots()\n", + "ax.grid()\n", + "plt.xlim(0,6)\n", + "plt.ylim(0,8)\n", + "for color, vector in [('green', a), ('blue', b)]:\n", + " plt.arrow(0, 0,\n", + " vector[0], vector[1],\n", + " head_width = .2,\n", + " head_length = .2, \n", + " linewidth = 2,\n", + " color = color)\n", + " \n", + "plt.arrow(b[0], b[1], \n", + " a_b [0], a_b[1],\n", + " head_width = .2,\n", + " head_length = .2, \n", + " linewidth = 2,\n", + " color = 'red',\n", + " alpha = .7)\n", + "\n", + "plt.show();" + ], + "execution_count": 51, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -195,13 +444,34 @@ "metadata": { "id": "2_cZQFCskYNr", "colab_type": "code", - "colab": {} + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "23ede11c-e045-41a1-9b78-6cb8d410af61" }, "source": [ - "" + "c = [7, 22, 4, 16]\n", + "d = [12, 6, 2, 9]\n", + "\n", + "dot = np.dot(c,d)\n", + "dot" ], - "execution_count": 0, - "outputs": [] + "execution_count": 52, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "368" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 52 + } + ] }, { "cell_type": "markdown", @@ -224,13 +494,36 @@ "metadata": { "id": "ku-TdCKAkYs8", "colab_type": "code", - "colab": {} + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "328a89c1-80bc-498a-aedf-6ab82420a3ba" }, "source": [ - "" + "e = [[5], [7], [2]]\n", + "f = [[3], [4], [6]]\n", + "\n", + "cross = np.cross(e,f,axis=0)\n", + "cross" ], - "execution_count": 0, - "outputs": [] + "execution_count": 54, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[ 34],\n", + " [-24],\n", + " [ -1]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 54 + } + ] }, { "cell_type": "markdown", @@ -253,13 +546,69 @@ "metadata": { "id": "-5VKOMKBlgaA", "colab_type": "code", - "colab": {} + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "232dce22-8596-46da-f0d4-fd0378b88c28" }, "source": [ - "" + "g = [[1], [1], [1], [8]]\n", + "h = [[3], [3], [3], [3]]\n", + "\n", + "norm_g = np.linalg.norm(g)\n", + "norm_h = np.linalg.norm(h)\n", + "\n", + "print(norm_g)\n", + "norm_h" ], - "execution_count": 0, - "outputs": [] + "execution_count": 56, + "outputs": [ + { + "output_type": "stream", + "text": [ + "8.18535277187245\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "6.0" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 56 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "69H42CjW3B9i", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "27166444-c9be-4d4a-e9a1-23d1fa95d5d5" + }, + "source": [ + "print('norm_g is longer than norm_h:', norm_g > norm_h)" + ], + "execution_count": 61, + "outputs": [ + { + "output_type": "stream", + "text": [ + "norm_g is longer than norm_h: True\n" + ], + "name": "stdout" + } + ] }, { "cell_type": "markdown", @@ -316,11 +665,264 @@ "colab": {} }, "source": [ - "" + "A = [[1,2], [3,4], [5,6]]\n", + "B = [[2,4,6]]\n", + "C = [[9,6,3], [4,7,11]]\n", + "D = [[1,0,0], [0,1,0], [0,0,1]]\n", + "E = [[1,3], [5,7]]" ], - "execution_count": 0, + "execution_count": 65, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "8uMvt8SPB989", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "709a3ee0-44b2-4011-cdcf-343973bee423" + }, + "source": [ + "np.matmul(A,E)" + ], + "execution_count": 63, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[11, 17],\n", + " [23, 37],\n", + " [35, 57]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 63 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "TLIMIHv8DB93", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "a4721a1d-0aaa-44ef-c2c5-cf82ce076cdb" + }, + "source": [ + "np.matmul(A,C)" + ], + "execution_count": 70, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[17, 20, 25],\n", + " [43, 46, 53],\n", + " [69, 72, 81]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 70 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "HLdGG0hEDMLG", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "f14a8f7a-e5e4-4da8-fb05-21a254f5de7d" + }, + "source": [ + "np.matmul(B,A)" + ], + "execution_count": 71, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[44, 56]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 71 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Vc4qrB7XC-cW", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "e252fe06-5217-4113-f635-431849c0f954" + }, + "source": [ + "np.matmul(B,D)" + ], + "execution_count": 69, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[2, 4, 6]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 69 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "UvvfIlx4DS2Y", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "8611128b-cd49-4885-bf72-08125e4f034c" + }, + "source": [ + "np.matmul(C,A)" + ], + "execution_count": 72, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[ 42, 60],\n", + " [ 80, 102]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 72 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "cnSw-QwHCGwP", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "fd0e9395-16dd-48bf-98f0-2d5375347345" + }, + "source": [ + "np.matmul(C,D)" + ], + "execution_count": 68, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[ 9, 6, 3],\n", + " [ 4, 7, 11]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 68 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "G1BM1QCeDZuE", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "019b077c-412c-4490-b819-e2566020b542" + }, + "source": [ + "np.matmul(D,A)" + ], + "execution_count": 74, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[1, 2],\n", + " [3, 4],\n", + " [5, 6]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 74 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "ShVWsV2WDjQV", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "48c4f8b3-e66a-4e24-b797-35684d3d493a" + }, + "source": [ + "np.matmul(E,C)" + ], + "execution_count": 75, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[21, 27, 36],\n", + " [73, 79, 92]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 75 + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -336,13 +938,177 @@ "metadata": { "id": "zhKwiSItoE2F", "colab_type": "code", - "colab": {} + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "1db7f4d7-4107-49a2-adc6-c582e59ecba4" }, "source": [ - "" + "np.matmul(C,D)[0][0]" ], - "execution_count": 0, - "outputs": [] + "execution_count": 76, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "9" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 76 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "c9aRPWSuEOkg", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "a1fa5736-b9ff-4d64-8f90-078d8ba8a145" + }, + "source": [ + "print(np.matmul(C,D).shape)\n", + "print('Number of rows in matrix C:', np.matmul(C,D).shape[0])\n", + "print('Number of cols in matrix D:', np.matmul(C,D).shape[1])" + ], + "execution_count": 84, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(2, 3)\n", + "Number of rows in matrix C: 2\n", + "Number of cols in matrix D: 3\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "c63Lc5HpEA5g", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "b9df7ad8-ab6a-4d6a-f3e0-404a144fd97b" + }, + "source": [ + "np.matmul(A,E)[0][0]" + ], + "execution_count": 77, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "11" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 77 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "yeOV6xqSERfK", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "dc1e96ae-58de-45ee-874b-f2742ae26a20" + }, + "source": [ + "print(np.matmul(A,E).shape)\n", + "print('Number of rows in matrix A:', np.matmul(A,E).shape[0])\n", + "print('Number of cols in matrix E:', np.matmul(A,E).shape[1])" + ], + "execution_count": 85, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(3, 2)\n", + "Number of rows in matrix A: 3\n", + "Number of cols in matrix E: 2\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "t0uuCBmSEEHA", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "57a40e39-9a52-4a14-ef24-4a861d0fb076" + }, + "source": [ + "np.matmul(B,A)[0][0]" + ], + "execution_count": 78, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "44" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 78 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "2cPh1_a-ETpR", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "3a993ff6-031f-4af1-d2e3-593aab7e39d7" + }, + "source": [ + "print(np.matmul(B,A).shape)\n", + "print('Number of rows in matrix B:', np.matmul(B,A).shape[0])\n", + "print('Number of cols in matrix A:', np.matmul(B,A).shape[1])" + ], + "execution_count": 87, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(1, 2)\n", + "Number of rows in matrix B: 1\n", + "Number of cols in matrix A: 2\n" + ], + "name": "stdout" + } + ] }, { "cell_type": "markdown", @@ -373,11 +1139,108 @@ "colab": {} }, "source": [ - "" + "F = [[20,19,18,17],\n", + " [16,15,14,13],\n", + " [12,11,10,9],\n", + " [8,7,6,5],\n", + " [4,3,2,1]]" ], - "execution_count": 0, + "execution_count": 93, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "Mx0UJ8YLFvta", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "56bb68c9-fef0-4d4e-e6e1-696aac3b549a" + }, + "source": [ + "np.array(F).shape" + ], + "execution_count": 90, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(5, 4)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 90 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "WDdfKlPiGBVO", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 85 + }, + "outputId": "7263caa5-82b1-48db-c14e-e67a617ef68f" + }, + "source": [ + "np.array(F).T" + ], + "execution_count": 94, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[20, 16, 12, 8, 4],\n", + " [19, 15, 11, 7, 3],\n", + " [18, 14, 10, 6, 2],\n", + " [17, 13, 9, 5, 1]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 94 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "YPkIs9A6GOc0", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "17605f5c-5691-4df5-e6d1-6b2571346bc0" + }, + "source": [ + "np.array(F).T.shape" + ], + "execution_count": 95, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(4, 5)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 95 + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -413,14 +1276,78 @@ "metadata": { "id": "ZnqvZBOYqar3", "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "44823a8e-4c80-4b02-b9e9-56e469959764" + }, + "source": [ + "G = [[13,14], [21,12]]\n", + "GI = np.linalg.inv(G)\n", + "GI" + ], + "execution_count": 103, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[-0.08695652, 0.10144928],\n", + " [ 0.15217391, -0.0942029 ]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 103 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "6XVZueI2IZc2", + "colab_type": "code", "colab": {} }, "source": [ - "" + "G_GI = np.matmul(G,GI)" ], - "execution_count": 0, + "execution_count": 107, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "KJ32_OXWJnzj", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "98bff35e-9a33-4e36-ab79-3cf75e7042e8" + }, + "source": [ + "np.matmul(G, G_GI)" + ], + "execution_count": 108, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[13., 14.],\n", + " [21., 12.]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 108 + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -454,11 +1381,72 @@ "colab": {} }, "source": [ - "" + "H = [[12,11], [7,10]]\n", + "J = [[0,1,2], [7,10,4], [3,2,0]]" ], - "execution_count": 0, + "execution_count": 109, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "g_oxmjIxKd13", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "affb5497-49b7-412e-fa7e-4ec0d6981ae5" + }, + "source": [ + "np.linalg.det(H)" + ], + "execution_count": 110, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "43.000000000000014" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 110 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Gt_3IljEKh9A", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "8dc62a6b-b0bc-424b-a787-7c0f4aa16933" + }, + "source": [ + "np.linalg.det(J)" + ], + "execution_count": 111, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "-19.999999999999996" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 111 + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -474,13 +1462,65 @@ "metadata": { "id": "nyX6De2-rio1", "colab_type": "code", - "colab": {} + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "5cc56f97-1d30-4b28-ef10-c250e8cd3d83" }, "source": [ - "" + "HI = np.linalg.inv(H)\n", + "HI" ], - "execution_count": 0, - "outputs": [] + "execution_count": 123, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[ 0.23255814, -0.25581395],\n", + " [-0.1627907 , 0.27906977]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 123 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "cPidyKspKo8Z", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "38c791f0-5349-4734-dfec-4eea3fbe24b3" + }, + "source": [ + "JI = np.linalg.inv(J)\n", + "JI" + ], + "execution_count": 127, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[ 0.4 , -0.2 , 0.8 ],\n", + " [-0.6 , 0.3 , -0.7 ],\n", + " [ 0.8 , -0.15, 0.35]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 127 + } + ] }, { "cell_type": "markdown", @@ -494,6 +1534,71 @@ "Please ignore Python rounding errors. If necessary, format your output so that it rounds to 5 significant digits (the fifth decimal place)." ] }, + { + "cell_type": "code", + "metadata": { + "id": "Eh6lJwAKKs8t", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "878aa8c7-b34f-4376-cd45-488689d28f15" + }, + "source": [ + "H_HI = np.matmul(H,HI)\n", + "H_HI" + ], + "execution_count": 125, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[1.00000000e+00, 5.55111512e-16],\n", + " [2.22044605e-16, 1.00000000e+00]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 125 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "VXt_TShZLR76", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "f292242d-86ea-441e-f44a-2eb4f7141464" + }, + "source": [ + "JI_J = np.matmul(JI,J)\n", + "JI_J" + ], + "execution_count": 128, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[ 1.00000000e+00, 2.22044605e-16, 0.00000000e+00],\n", + " [-1.11022302e-16, 1.00000000e+00, 0.00000000e+00],\n", + " [-1.66533454e-16, -1.11022302e-16, 1.00000000e+00]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 128 + } + ] + }, { "cell_type": "markdown", "metadata": { diff --git a/module2-intermediate-linear-algebra/LS_DS_132_Intermediate_Linear_Algebra_Assignment.ipynb b/module2-intermediate-linear-algebra/LS_DS_132_Intermediate_Linear_Algebra_Assignment.ipynb index 9110b2b1..bf76ea3c 100644 --- a/module2-intermediate-linear-algebra/LS_DS_132_Intermediate_Linear_Algebra_Assignment.ipynb +++ b/module2-intermediate-linear-algebra/LS_DS_132_Intermediate_Linear_Algebra_Assignment.ipynb @@ -33,6 +33,32 @@ "## 1.1 Sales for the past week was the following amounts: [3505, 2400, 3027, 2798, 3700, 3250, 2689]. Without using library functions, what is the mean, variance, and standard deviation of of sales from last week? (for extra bonus points, write your own function that can calculate these two values for any sized list)" ] }, + { + "cell_type": "code", + "metadata": { + "id": "Nwoao48vCAON", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import math" + ], + "execution_count": 116, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "v5_-pvlj8LYT", + "colab_type": "code", + "colab": {} + }, + "source": [ + "past_week_sales = [3505, 2400, 3027, 2798, 3700, 3250, 2689]" + ], + "execution_count": 117, + "outputs": [] + }, { "cell_type": "code", "metadata": { @@ -41,11 +67,69 @@ "colab": {} }, "source": [ - "" + "def calculate_mean(list):\n", + " length = len(list)\n", + " total = sum(list)\n", + " mean = total/length\n", + " return mean\n", + "\n", + "def calculate_variance(list):\n", + " distances = []\n", + " mean = calculate_mean(list)\n", + " for el in list:\n", + " distance = (el - mean)**2\n", + " distances.append(distance)\n", + " varience = sum(distances)\n", + " return varience \n", + "\n", + "\n", + "def calculate_std(list):\n", + " std = math.sqrt(calculate_variance(list))\n", + " return std" ], - "execution_count": 0, + "execution_count": 118, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "dWiwDkmLBepk", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "b284f12f-4cc9-476e-94cc-c4b672042850" + }, + "source": [ + "print(calculate_mean(past_week_sales))\n", + "print(calculate_variance(past_week_sales))\n", + "calculate_std(past_week_sales)" + ], + "execution_count": 119, + "outputs": [ + { + "output_type": "stream", + "text": [ + "3052.714285714286\n", + "1286327.4285714284\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "1134.1637573875425" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 119 + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -56,6 +140,20 @@ "## 1.2 Find the covariance between last week's sales numbers and the number of customers that entered the store last week: [127, 80, 105, 92, 120, 115, 93] (you may use librray functions for calculating the covariance since we didn't specifically talk about its formula)" ] }, + { + "cell_type": "code", + "metadata": { + "id": "K0j8HgaxGzrY", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import numpy as np\n", + "import pandas as pd" + ], + "execution_count": 120, + "outputs": [] + }, { "cell_type": "code", "metadata": { @@ -64,11 +162,103 @@ "colab": {} }, "source": [ - "" + "past_week_customers = [127, 80, 105, 92, 120, 115, 93]" + ], + "execution_count": 121, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "A48lYDJaD3q2", + "colab_type": "code", + "colab": {} + }, + "source": [ + "def calculate_covarience(list_x, list_y):\n", + " if len(list_x)== len(list_y):\n", + " n = len(list_x)\n", + " mean_x = calculate_mean(list_x)\n", + " mean_y = calculate_mean(list_y)\n", + " distances_x = []\n", + " distances_y = []\n", + " for el_x in list_x:\n", + " distance_x = el_x - mean_x\n", + " distances_x.append(distance_x)\n", + " for el_y in list_y:\n", + " distance_y = el_y - mean_y\n", + " distances_y.append(distance_y)\n", + " for num in range(n):\n", + " mul_x_y = np.array(distances_x)*np.array(distances_y)\n", + " covarience = sum(mul_x_y)/(n-1)\n", + " return covarience\n", + " else: \n", + " print('Lists are not equal')" ], - "execution_count": 0, + "execution_count": 122, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "4STbdf1IHLUe", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "349ea98a-546b-4f3f-ca15-8929ca12baae" + }, + "source": [ + "calculate_covarience(past_week_sales, past_week_customers)" + ], + "execution_count": 123, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "7604.357142857142" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 123 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "U9DDXZMBQ74X", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "4a69ac77-ef36-4a7e-ba0d-188b85a2c7a4" + }, + "source": [ + "np.cov(past_week_sales, past_week_customers)" + ], + "execution_count": 124, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[214387.9047619 , 7604.35714286],\n", + " [ 7604.35714286, 290.95238095]])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 124 + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -87,11 +277,45 @@ "colab": {} }, "source": [ - "" + "def calculate_corr(list_x, list_y):\n", + " std_x = calculate_std(list_x)\n", + " std_y = calculate_std(list_y)\n", + " corr = calculate_covarience(list_x, list_y)/(std_x*std_y)\n", + " return corr" ], - "execution_count": 0, + "execution_count": 140, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "xkCP8V3sPwWh", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "114b7e62-5eb7-4e7e-f014-69646c9e3556" + }, + "source": [ + "calculate_corr(past_week_sales, past_week_customers)" + ], + "execution_count": 141, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0.16047232963581515" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 141 + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -109,13 +333,494 @@ "metadata": { "id": "0TWgUIiaCFzq", "colab_type": "code", - "colab": {} + "colab": { + "base_uri": "https://localhost:8080/", + "height": 530 + }, + "outputId": "a6d84e62-42ee-4910-ad38-f31ec662c771" }, "source": [ - "" + "url = 'https://raw.githubusercontent.com/Geoyi/Cleaning-Titanic-Data/master/titanic_clean.csv'\n", + "titanic = pd.read_csv(url, usecols=range(1,16))\n", + "titanic.head()" ], - "execution_count": 0, - "outputs": [] + "execution_count": 127, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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pclasssurvivednamesexagesibspparchticketfarecabinembarkedboatbodyhome.desthas_cabin_number
01.01.0Allen, Miss. Elisabeth Waltonfemale29.00000.00.024160211.3375B5S2NaNSt Louis, MO1
11.01.0Allison, Master. Hudson Trevormale0.91671.02.0113781151.5500C22 C26S11NaNMontreal, PQ / Chesterville, ON1
21.00.0Allison, Miss. Helen Lorainefemale2.00001.02.0113781151.5500C22 C26SNaNNaNMontreal, PQ / Chesterville, ON1
31.00.0Allison, Mr. Hudson Joshua Creightonmale30.00001.02.0113781151.5500C22 C26SNaN135.0Montreal, PQ / Chesterville, ON1
41.00.0Allison, Mrs. Hudson J C (Bessie Waldo Daniels)female25.00001.02.0113781151.5500C22 C26SNaNNaNMontreal, PQ / Chesterville, ON1
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" + ], + "text/plain": [ + " pclass survived ... home.dest has_cabin_number\n", + "0 1.0 1.0 ... St Louis, MO 1\n", + "1 1.0 1.0 ... Montreal, PQ / Chesterville, ON 1\n", + "2 1.0 0.0 ... Montreal, PQ / Chesterville, ON 1\n", + "3 1.0 0.0 ... Montreal, PQ / Chesterville, ON 1\n", + "4 1.0 0.0 ... Montreal, PQ / Chesterville, ON 1\n", + "\n", + "[5 rows x 15 columns]" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 127 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "u1RP8fbOQQNb", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 297 + }, + "outputId": "a411d807-6262-4dae-8142-49eefd5f1d90" + }, + "source": [ + "titanic.cov()" + ], + "execution_count": 128, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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pclasssurvivedagesibspparchfarebodyhas_cabin_number
pclass0.701969-0.127248-3.9546050.0530900.013287-24.227788-2.876653-0.249992
survived-0.1272480.236250-0.314343-0.0140880.0347766.1460230.0000000.061406
age-3.954605-0.314343165.850021-2.559806-1.459378114.41661381.6229221.463138
sibsp0.053090-0.014088-2.5598061.0850520.3368338.641768-8.708471-0.003946
parch0.0132870.034776-1.4593780.3368330.7491959.9280314.2371900.013316
fare-24.2277886.146023114.4166138.6417689.9280312678.959738-179.16468410.976961
body-2.8766530.00000081.622922-8.7084714.237190-179.1646849544.6885673.625689
has_cabin_number-0.2499920.0614061.463138-0.0039460.01331610.9769613.6256890.174613
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pclasssurvivedagesibspparchfarebodyhas_cabin_number
pclass1.000000-0.312469-0.3663700.0608320.018322-0.558629-0.034642-0.713857
survived-0.3124691.000000-0.050199-0.0278250.0826600.244265NaN0.302250
age-0.366370-0.0501991.000000-0.190747-0.1308720.1718920.0590590.271887
sibsp0.060832-0.027825-0.1907471.0000000.3735870.160238-0.099961-0.009064
parch0.0183220.082660-0.1308720.3735871.0000000.2215390.0510990.036806
fare-0.5586290.2442650.1718920.1602380.2215391.000000-0.0431100.507253
body-0.034642NaN0.059059-0.0999610.051099-0.0431101.0000000.083796
has_cabin_number-0.7138570.3022500.271887-0.0090640.0368060.5072530.0837961.000000
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" + ], + "text/plain": [ + " pclass survived ... body has_cabin_number\n", + "pclass 1.000000 -0.312469 ... -0.034642 -0.713857\n", + "survived -0.312469 1.000000 ... NaN 0.302250\n", + "age -0.366370 -0.050199 ... 0.059059 0.271887\n", + "sibsp 0.060832 -0.027825 ... -0.099961 -0.009064\n", + "parch 0.018322 0.082660 ... 0.051099 0.036806\n", + "fare -0.558629 0.244265 ... -0.043110 0.507253\n", + "body -0.034642 NaN ... 1.000000 0.083796\n", + "has_cabin_number -0.713857 0.302250 ... 0.083796 1.000000\n", + "\n", + "[8 rows x 8 columns]" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 129 + } + ] }, { "cell_type": "markdown", @@ -140,16 +845,58 @@ { "cell_type": "code", "metadata": { - "id": "YLSBk7hJvvCx", + "id": "Et5mnqooUIUv", "colab_type": "code", "colab": {} }, "source": [ - "" + "import matplotlib.pyplot as plt" ], - "execution_count": 0, + "execution_count": 138, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "YLSBk7hJvvCx", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 390 + }, + "outputId": "f9486939-9bd3-441c-9678-36792fec935a" + }, + "source": [ + "x = [0,3]\n", + "y = [1,0]\n", + "\n", + "fig, ax = plt.subplots(figsize = (6,6))\n", + "plt.xlim = (-2,4)\n", + "plt.ylim = (-2,4)\n", + "\n", + "plt.arrow(0,0, x[0], x[1], head_length = .2, head_width = .2, color = 'c')\n", + "plt.arrow(0,0, y[0], y[1], head_length = .2, head_width = .2, color = 'r')\n", + "\n", + "plt.title(\"Orthogonal(Perpendicular) Vectors\")\n", + "plt.show;" + ], + "execution_count": 148, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -174,9 +921,40 @@ "colab": {} }, "source": [ - "" + "a = [-5,3,7]\n", + "b = [6, -8, 2]" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "JVzxMrZGVnka", + "colab_type": "code", + "colab": {} + }, + "source": [ + "def are_orthogonal(x,y):\n", + " if np.dot(x,y) == 0:\n", + " print('Vectors are orthogonal')\n", + " else:\n", + " print('Vectors are NOT orthogonal')" ], - "execution_count": 0, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "al2viJLAWH2g", + "colab_type": "code", + "colab": {} + }, + "source": [ + "are_orthogonal(a,b)" + ], + "execution_count": null, "outputs": [] }, { @@ -207,9 +985,24 @@ "colab": {} }, "source": [ - "" + "c = np.array([2, -15, 6, 20])" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "89Ak7JF6WgB_", + "colab_type": "code", + "colab": {} + }, + "source": [ + "print('||c|| :', np.linalg.norm(c)**2)\n", + "print('c dot c :', np.dot(c,c))\n", + "print('c^T c :', np.matmul(c.T, c))" ], - "execution_count": 0, + "execution_count": null, "outputs": [] }, { @@ -245,7 +1038,40 @@ "colab_type": "text" }, "source": [ - "Your text here" + "##Vector d:\n", + "\\begin{align}\n", + "||d|| = \n", + "\\sqrt{7^2 + 12^2}\n", + "\\\\\n", + "\\\\\n", + "||d|| = \n", + "13,89\n", + "\\\\\n", + "\\\\\n", + " \\hat{d} = \\frac{1}{||d||}d = \\frac{1}{13,89}\\begin{bmatrix} 7 \\\\ 12 \\end{bmatrix} = \\begin{bmatrix} 0,5 \\\\ 0,86 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "d = 13,89 \\begin{bmatrix} 0,5 \\\\ 0,86 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "\\\\\n", + "\\end{align}\n", + "##Vector e:\n", + "\\begin{align}\n", + "||e|| = \n", + "\\sqrt{2^2 + 11^2 + (-8)^2}\n", + "\\\\\n", + "\\\\\n", + "||e|| = \n", + "13,75\n", + "\\\\\n", + "\\\\\n", + " \\hat{e} = \\frac{1}{||e||}e = \\frac{1}{13,75}\\begin{bmatrix} 7 \\\\ 11 \\\\ -8 \\end{bmatrix} = \\begin{bmatrix} 0,51 \\\\ 0,8 \\\\ -0,58 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "e = 13,75 \\begin{bmatrix} 0,51 \\\\ 0,8 \\\\ -0,58 \\end{bmatrix}\n", + "\\end{align}\n", + "\n" ] }, { @@ -270,9 +1096,36 @@ "colab": {} }, "source": [ - "" + "f = np.array([4, 12, 11, 9, 2])" ], - "execution_count": 0, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "_qlGbjxni8xr", + "colab_type": "code", + "colab": {} + }, + "source": [ + "norm_f = np.linalg.norm(f)" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "iMiynI3xjIms", + "colab_type": "code", + "colab": {} + }, + "source": [ + "unit_f = f/norm_f\n", + "unit_f" + ], + "execution_count": null, "outputs": [] }, { @@ -295,6 +1148,116 @@ "## 4.1 Plot two vectors that are linearly dependent and two vectors that are linearly independent (bonus points if done in $\\mathbb{R}^3$)." ] }, + { + "cell_type": "code", + "metadata": { + "id": "DFkb89NqYVpN", + "colab_type": "code", + "colab": {} + }, + "source": [ + "x_dep = [2,4]\n", + "y_dep = [1,2]" + ], + "execution_count": 154, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "Bd2ZJnuSYggU", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 269 + }, + "outputId": "a049e076-81a7-41c6-a5bf-3a520cc63ef6" + }, + "source": [ + "fig, ax = plt.subplots(figsize=(4,4))\n", + "ax.grid()\n", + "plt.xlim(0,5)\n", + "plt.ylim(0,5)\n", + "plt.arrow(0,0,x_dep[0],x_dep[1],\n", + " head_width = .2, head_length = .2, \n", + " color = 'r')\n", + "plt.arrow(0,0,y_dep[0],y_dep[1],\n", + " head_width = .2, head_length = .2, \n", + " color = 'c')\n", + "plt.show();" + ], + "execution_count": 155, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "dSQ7NO8zhkSs", + "colab_type": "code", + "colab": {} + }, + "source": [ + "x_indep = [2,3]\n", + "y_indep = [1,2]" + ], + "execution_count": 152, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "vYwUbe3hhkGr", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 269 + }, + "outputId": "7224ca89-dd60-42b0-b5da-2af141d7a127" + }, + "source": [ + "fig, ax = plt.subplots(figsize=(4,4))\n", + "ax.grid()\n", + "plt.xlim(0,5)\n", + "plt.ylim(0,5)\n", + "plt.arrow(0,0,x_indep[0],x_indep[1],\n", + " head_width = .2, head_length = .2, \n", + " color = 'r')\n", + "plt.arrow(0,0,y_indep[0],y_indep[1],\n", + " head_width = .2, head_length = .2, \n", + " color = 'c')\n", + "plt.show();" + ], + "execution_count": 151, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, { "cell_type": "markdown", "metadata": { @@ -329,9 +1292,25 @@ "colab": {} }, "source": [ - "" + "g = np.array([1,2])\n", + "h = np.array([4,8])" ], - "execution_count": 0, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "bRpLj2dQjjzb", + "colab_type": "code", + "colab": {} + }, + "source": [ + "(g/h)[0] == (g/h)[1]\n", + "# if True vectors lie on the same line\n", + "# meaning span of two vectors is a line" + ], + "execution_count": null, "outputs": [] }, { @@ -360,9 +1339,33 @@ "colab": {} }, "source": [ - "" + "l = np.array([1,2,3])\n", + "m = np.array([-1,0, 7])\n", + "n = np.array([4,8,2])" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "1e5CC80wlDBs", + "colab_type": "code", + "colab": {} + }, + "source": [ + "matrix = np.array(\n", + " [\n", + " [1, 2 ,3 ],\n", + " [-1, 0, 7],\n", + " [4, 8, 2]\n", + " ])\n", + "\n", + "m/l/n\n", + "# neither of three vectors can be represented by another => \n", + "# span of three vectors is R3" ], - "execution_count": 0, + "execution_count": null, "outputs": [] }, { @@ -394,9 +1397,29 @@ "colab": {} }, "source": [ - "" + "t = [5,3]\n", + "p = [-2, 6]" ], - "execution_count": 0, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "kJ2tEPQvy56h", + "colab_type": "code", + "colab": {} + }, + "source": [ + "fig, ax = plt.subplots(figsize=(4,4))\n", + "ax.grid()\n", + "plt.xlim(-4,7)\n", + "plt.ylim(-4,7)\n", + "for vect in [t,p]:\n", + " plt.arrow(0,0, vect[0], vect[1], \n", + " head_length = .2, head_width = .2)" + ], + "execution_count": null, "outputs": [] }, { @@ -416,7 +1439,7 @@ "colab_type": "text" }, "source": [ - "" + "To form a basis for some space V means to span the space V. Two vectors form basis for $\\mathbb{R}^2$ if they are linearly independant, neither of two vectors can represented by another." ] }, { @@ -447,6 +1470,60 @@ "\\end{align}" ] }, + { + "cell_type": "code", + "metadata": { + "id": "O7H_2_lG3L-g", + "colab_type": "code", + "colab": {} + }, + "source": [ + "P = [\n", + " [1,2,3],\n", + " [-1,0,7],\n", + " [4,8,2]\n", + "]" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "mFExV8UO3Vz6", + "colab_type": "code", + "colab": {} + }, + "source": [ + "# substract the first row from the second row\n", + "P = [\n", + " [1,2,3],\n", + " [0,2,10],\n", + " [4,8,2]\n", + "]\n", + "# substract the first row 4 times from the third row\n", + "P = [\n", + " [1,2,3],\n", + " [0,2,10],\n", + " [0,0,-10]\n", + "]\n", + "# multiply the second row by 1/2\n", + "P = [\n", + " [1,2,3],\n", + " [0,1,5],\n", + " [0,0,-10]\n", + "]\n", + "# multiply the thrid row by -1/10\n", + "P = [\n", + " [1,2,3],\n", + " [0,1,5],\n", + " [0,0,1]\n", + "]\n", + "# matrix has no zero rows => Rank(P) = 3" + ], + "execution_count": null, + "outputs": [] + }, { "cell_type": "markdown", "metadata": { @@ -464,7 +1541,7 @@ "colab_type": "text" }, "source": [ - "" + "Rank of a matrix tells us which dimensionality has space ranked by its columns." ] }, { @@ -498,9 +1575,51 @@ "colab": {} }, "source": [ - "" + "v = np.array([1,3])\n", + "w = np.array([-1,2])" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "htR8Yj7B69j9", + "colab_type": "code", + "colab": {} + }, + "source": [ + "c = np.dot(w,v)/np.dot(v,v)\n", + "proj_w = c*v\n", + "c" ], - "execution_count": 0, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "sdLfLLad7oPw", + "colab_type": "code", + "colab": {} + }, + "source": [ + "fig, ax = plt.subplots(figsize=(6,6))\n", + "ax.grid()\n", + "plt.xlim(-2, 4)\n", + "plt.ylim(-2, 4)\n", + "\n", + "x_vals = np.array(ax.get_xlim())\n", + "y_vals = x_vals*3\n", + "plt.plot(x_vals, y_vals, '--', color='r', linewidth=1)\n", + "\n", + "for vect, color in [(v,'red'), (w,'blue'), (proj_w,'gray')]:\n", + " plt.arrow(0,0, vect[0], vect[1],\n", + " head_length = .2, head_width= .2,\n", + " color = color)\n", + "plt.show();" + ], + "execution_count": null, "outputs": [] }, { @@ -524,41 +1643,49 @@ "metadata": { "id": "cp52kZra-ykj", "colab_type": "code", - "outputId": "12502200-eafe-4e20-bfb7-2d539c6027cb", "colab": { "base_uri": "https://localhost:8080/", - "height": 347 - } + "height": 374 + }, + "outputId": "c40356de-1044-4823-ae60-f955fc33a802" }, "source": [ "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "# Creating a dataframe for you to work with -Feel free to not use the dataframe if you don't want to.\n", - "x_values = [1, 4, 7, 3, 9, 4, 5 ]\n", + "x_values = [1, 4, 7, 3, 9, 4, 5]\n", "y_values = [4, 2, 5, 0, 8, 2, 8]\n", "\n", "data = {\"x\": x_values, \"y\": y_values}\n", "\n", "df = pd.DataFrame(data)\n", "\n", - "df.head()\n", + "fig, ax = plt.subplots(figsize = (6,6))\n", + "plt.xlim = (0,9)\n", + "plt.ylim = (0,9)\n", + "\n", + "plt.plot([0,9], [0,9], '--', color='r', linewidth=1)\n", + "\n", + "df1 = projection_to_xy(x_values, y_values)\n", "\n", "plt.scatter(df.x, df.y)\n", + "plt.scatter(df1.x, df1.y)\n", "plt.show()" ], - "execution_count": 0, + "execution_count": 179, "outputs": [ { "output_type": "display_data", "data": { - "image/png": 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\n", 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" ] }, "metadata": { - "tags": [] + "tags": [], + "needs_background": "light" } } ] @@ -570,10 +1697,38 @@ "colab_type": "code", "colab": {} }, + "source": [ + "def projection_to_xy(x,y):\n", + " xy = np.array([1,1])\n", + " x = np.array(x)\n", + " y = np.array(y)\n", + " x_col = []\n", + " y_col = []\n", + " for num in range(0,7) :\n", + " vect = [x[num], y[num]]\n", + " c = np.dot(vect,xy)/np.dot(xy,xy)\n", + " proj_vect = c*xy\n", + " x_col.append(proj_vect[0])\n", + " y_col.append(proj_vect[1])\n", + " data1 = {\"x\": x_col, \"y\": y_col}\n", + " df1 = pd.DataFrame(data1)\n", + " return df1\n", + " \n" + ], + "execution_count": 177, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "2O_0AouNxCA_", + "colab_type": "code", + "colab": {} + }, "source": [ "" ], - "execution_count": 0, + "execution_count": null, "outputs": [] } ] diff --git a/module3-dimensionality-reductionCopy_of_LS_DS_133_High_Dimensional_Data_Assignment.ipynb b/module3-dimensionality-reductionCopy_of_LS_DS_133_High_Dimensional_Data_Assignment.ipynb new file mode 100644 index 00000000..a5665680 --- /dev/null +++ b/module3-dimensionality-reductionCopy_of_LS_DS_133_High_Dimensional_Data_Assignment.ipynb @@ -0,0 +1,1975 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "Copy of LS_DS_133_High_Dimensional_Data_Assignment.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7wMWCkE1RZpM", + "colab_type": "text" + }, + "source": [ + "# Vertical Line Test" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "W0-g7aprRv2j", + "colab_type": "text" + }, + "source": [ + "## 1.1 Create two graphs, one that passes the vertical line test and one that does not." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "fIJhCtF6RW_U", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import pandas as pd \n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "plt.rcParams.update({'font.size': 14})" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "NPbV1f_4yqZt", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "outputId": "15573b2d-4f28-4499-913a-cf936ec51e14" + }, + "source": [ + "x = np.arange(-11,11)\n", + "y = x*2\n", + "plt.plot(x,y)\n", + "plt.axvline(x=0, color='r');" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Ky1TDoL1zGxS", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "outputId": "c9d95297-39dc-4e74-9f66-da0018f6a4a9" + }, + "source": [ + "y = np.arange(-3,3)\n", + "x = np.cos(y) \n", + "plt.plot(x,y)\n", + "plt.axvline(x=0, color='r');" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ckeTKqMgRy7g", + "colab_type": "text" + }, + "source": [ + "## 1.2 Why are graphs that don't pass the vertical line test not considered \"functions?\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Gtl20YeDR6x-", + "colab_type": "text" + }, + "source": [ + "Function is defined as a relation between a set of inputs and a set of outputs where each input is related to only one output" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "g21uN62xSKSk", + "colab_type": "text" + }, + "source": [ + "# Functions as Relations" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gwkcV-EMSMNd", + "colab_type": "text" + }, + "source": [ + "## 2.1 Which of the following relations are functions? Why?\n", + "\n", + "\\begin{align}\n", + "\\text{Relation 1: } \\{(1, 2), (3, 2), (1, 3)\\}\n", + "\\\\\n", + "\\text{Relation 2: } \\{(1, 3), (2, 3), (6, 7)\\}\n", + "\\\\\n", + "\\text{Relation 3: } \\{(9, 4), (2, 1), (9, 6)\\}\n", + "\\\\\n", + "\\text{Relation 4: } \\{(6, 2), (8, 3), (6, 4)\\}\n", + "\\\\\n", + "\\text{Relation 5: } \\{(2, 6), (2, 7), (2, 4)\\}\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Dne86CPc2gLO", + "colab_type": "text" + }, + "source": [ + "Relation 2 is a functoin, because each x-value is associated with only one y-value\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "y0U30PrlTAAa", + "colab_type": "text" + }, + "source": [ + "# Functions as a mapping between dimensions\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "pw-OU9qmT5Ua", + "colab_type": "text" + }, + "source": [ + "## 3.1 for the following functions what is the dimensionality of the domain (input) and codomain (range/output)?\n", + "\n", + "\\begin{align}\n", + "m(𝑥_1,𝑥_2,𝑥_3)=(x_1+x_2, x_1+x_3, x_2+x_3)\n", + "\\\\\n", + "\\mathbb{R}^3 to \\mathbb{R}^3\n", + "\\\\\n", + "n(𝑥_1,𝑥_2,𝑥_3,𝑥_4)=(x_2^2 + x_3, x_2x_4)\n", + "\\\\\n", + "\\mathbb{R}^4 to \\mathbb{R}^2\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "k4tKHjdHUevC", + "colab_type": "text" + }, + "source": [ + "## 3.2 Do you think it's possible to create a function that maps from a lower dimensional space to a higher dimensional space? If so, provide an example." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "eESiRcX88QoZ", + "colab_type": "text" + }, + "source": [ + "\\begin{align}\n", + "k(𝑥_1)=(x_1+x_1, x_1x_1)\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "2nEWvwVyVWdW", + "colab_type": "text" + }, + "source": [ + "# Vector Transformations" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1n0-6FsYVcVk", + "colab_type": "text" + }, + "source": [ + "## 4.1 Plug the corresponding unit vectors into each function. Use the output vectors to create a transformation matrix.\n", + "\n", + "\\begin{align}\n", + "p(\\begin{bmatrix}x_1 \\\\ x_2 \\end{bmatrix}) = \\begin{bmatrix} x_1 + 3x_2 \\\\2 x_2 - x_1 \\\\ \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "q(\\begin{bmatrix}x_1 \\\\ x_2 \\\\ x_3\\end{bmatrix}) = \\begin{bmatrix} 4x_1 + x_2 + 2x_3 \\\\2 x_2 - x_1 + 3x_3 \\\\ 5x_1 - 2x_3 + x_2 \\end{bmatrix}\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JoxYW865AU7u", + "colab_type": "text" + }, + "source": [ + "\\begin{align}\n", + "p(\\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}) = \\begin{bmatrix} 1 \\\\ 3 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "p(\\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}) = \\begin{bmatrix} -1 \\\\ 2 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "P = \\begin{bmatrix} 1 & 3 \\\\ -1 & 2 \\end{bmatrix}\n", + "\\\\\n", + "\\\\\n", + "q(\\begin{bmatrix} 1 \\\\ 0 \\\\ 0\\end{bmatrix}) = \\begin{bmatrix} 4 \\\\ 1 \\\\ 2\\end {bmatrix}\n", + "\\\\\n", + "\\\\\n", + "q(\\begin{bmatrix} 0 \\\\ 1 \\\\ 0\\end{bmatrix}) = \\begin{bmatrix} -1 \\\\ 2 \\\\ 3\\end {bmatrix}\n", + "\\\\\n", + "\\\\\n", + "q(\\begin{bmatrix} 0 \\\\ 0 \\\\ 1\\end{bmatrix}) = \\begin{bmatrix} 5 \\\\ 1 \\\\ -2\\end {bmatrix}\n", + "\\\\\n", + "\\\\\n", + "Q = \\begin{bmatrix} 4 & 1 & 2 \\\\ -1 & 2 & 3 \\\\ 5 & 1 & -2 \\end{bmatrix}\n", + "\\end{align}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "n5HUOQIxZ2gp", + "colab_type": "text" + }, + "source": [ + "## 4.2 Verify that your transformation matrices are correct by choosing an input matrix and calculating the result both via the traditional functions above and also via vector-matrix multiplication." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "K5US0u1HLyRD", + "colab_type": "text" + }, + "source": [ + "\\begin{align}\n", + "p(\\begin{bmatrix} 2 \\\\ 5 \\end{bmatrix}) = \\begin{bmatrix} 17 \\\\ 8 \\end{bmatrix}\n", + "\\end{align}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "0UANR1IEaVWE", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "c8774fb2-2ba0-480f-fd26-5145cdf2bcfc" + }, + "source": [ + "P = [[1, 3], [-1, 2]]\n", + "vec = [2, 5]\n", + "np.matmul(P,vec)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([17, 8])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 30 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JOs_SMK0NPYA", + "colab_type": "text" + }, + "source": [ + "\\begin{align}\n", + "q(\\begin{bmatrix} 2 \\\\ 1 \\\\ -1 \\end{bmatrix}) = \\begin{bmatrix} 7 \\\\ -3 \\\\ 13\\end{bmatrix}\n", + "\\end{align}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "7W8hwnD4NNQ7", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "2464d024-315f-4ba3-a606-0f29332a303a" + }, + "source": [ + "Q = [[4, 1, 2], [-1, 2, 3], [5, 1, -2]]\n", + "vec1 = [2, 1, -1]\n", + "np.matmul(Q, vec1)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([ 7, -3, 13])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 31 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vEoiri3mak7j", + "colab_type": "text" + }, + "source": [ + "# Eigenvalues and Eigenvectors" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5HY0R4u7anIr", + "colab_type": "text" + }, + "source": [ + "## 5.1 In your own words, give an explanation for the intuition behind eigenvalues and eigenvectors." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "de9N17UsaJhX", + "colab_type": "text" + }, + "source": [ + "Eigenvector is a vector that does not change its orientation during transformation described in a transformation matrix.\n", + "\n", + "Eigenvalue is a scaler which indicates how eigenvector was squished or streched during the transformation." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VdehMwBtatKI", + "colab_type": "text" + }, + "source": [ + "# The Curse of Dimensionality" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4oVrJax-a3SK", + "colab_type": "text" + }, + "source": [ + "## 6.1 What are some of the challenges of working with high dimensional spaces?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BMWAGSgpdP2B", + "colab_type": "text" + }, + "source": [ + "- It is hard for human brain to imagine n-dimensional space, thus it is hard to visualize n-dimentional data\n", + "\n", + "- Extra dimensions are expenssive to process but add less value, at some point it gets less cost effective to \n", + "\n", + "- At a high-dimensional space all data points appear to be more or less equidistant to one another, this harms algoriths that rely upon distance \n", + "\n", + "- When the number of parameters is greater than the number of instances, an extreme risk of overfitting the model occures. The model will no longer fit the signal or phenomen, but the noise or varience" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ZiBJxsZla88c", + "colab_type": "text" + }, + "source": [ + "## 6.2 What is the rule of thumb for how many observations you should have compared to parameters in your model?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ETWnO-17lfrL", + "colab_type": "text" + }, + "source": [ + "Make sure the number of obsevations is five time number of features" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "NZmqdeygbHJx", + "colab_type": "text" + }, + "source": [ + "# Principal Component Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7iEheetpbJdN", + "colab_type": "text" + }, + "source": [ + "## 7.1 Code for loading and cleaning the 2013 national dataset from the [Housing Affordability Data System (HADS)](https://www.huduser.gov/portal/datasets/hads/hads.html) --housing data, can be found below. \n", + "\n", + "## Perform PCA on the processed dataset `national_processed` (Make sure you standardize your data!) and then make a scatterplot of PC1 against PC2. Some of our discussion and work around PCA with this dataset will continue during tomorrow's lecture and assignment.\n", + "\n", + "Not only does this dataset have decent amount columns to begin with (99), but in preparing the data for PCA we have also [one-hot-encoded](https://hackernoon.com/what-is-one-hot-encoding-why-and-when-do-you-have-to-use-it-e3c6186d008f#targetText=One%20hot%20encoding%20is%20a,the%20entry%20in%20the%20dataset.) all of the categorical variables. This has the effect of creating a new column for each individual category of each categorical variable. After processing this dataset has 64738 columns. --Das a lot of columns.\n", + "\n", + "Don't worry too much about the mechanics of one-hot encoding right now, you will learn and experiment with a whole bunch of categorical encoding approaches in unit 2. \n", + "\n", + "The code below will read in the dataset and perform the one-hot encoding of the categorical variables. Start adding your PCA code at the bottom of the provided code." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Us4nNFs02HlD", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 355 + }, + "outputId": "eaae2ad7-5cce-4cdf-8231-6e86dc581f24" + }, + "source": [ + "from urllib.request import urlopen\n", + "from zipfile import ZipFile\n", + "from io import BytesIO\n", + "import os.path\n", + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Read Natinal Data \n", + "national_url = 'https://www.huduser.gov/portal/datasets/hads/hads2013n_ASCII.zip'\n", + "national_file = 'thads2013n.txt'\n", + "\n", + "if os.path.exists(national_file):\n", + " national = pd.read_csv(national_file)\n", + "else: \n", + " z_national = urlopen(national_url)\n", + " zip_national = ZipFile(BytesIO(z_national.read())).extract(national_file)\n", + " national = pd.read_csv(zip_national)\n", + "\n", + "print(national.shape)\n", + "national.head()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(64535, 99)\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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CONTROLAGE1METRO3REGIONLMEDFMRL30L50L80IPOVBEDRMSBUILTSTATUSTYPEVALUEVACANCYTENURENUNITSROOMSWEIGHTPERZINC2ZADEQZSMHCSTRUCTURETYPEOWNRENTUTILITYOTHERCOSTCOST06COST12COST08COSTMEDTOTSALASSISTEDGLMEDGL30GL50GL80APLMEDABL30...COST08RELPOVCATCOST08RELFMRPCTCOST08RELFMRCATCOST12RELAMIPCTCOST12RELAMICATCOST12RELPOVPCTCOST12RELPOVCATCOST12RELFMRPCTCOST12RELFMRCATCOSTMedRELAMIPCTCOSTMedRELAMICATCOSTMedRELPOVPCTCOSTMedRELPOVCATCOSTMedRELFMRPCTCOSTMedRELFMRCATFMTZADEQFMTMETRO3FMTBUILTFMTSTRUCTURETYPEFMTBEDRMSFMTOWNRENTFMTCOST06RELPOVCATFMTCOST08RELPOVCATFMTCOST12RELPOVCATFMTCOSTMEDRELPOVCATFMTINCRELPOVCATFMTCOST06RELFMRCATFMTCOST08RELFMRCATFMTCOST12RELFMRCATFMTCOSTMEDRELFMRCATFMTINCRELFMRCATFMTCOST06RELAMICATFMTCOST08RELAMICATFMTCOST12RELAMICATFMTCOSTMEDRELAMICATFMTINCRELAMICATFMTASSISTEDFMTBURDENFMTREGIONFMTSTATUS
0'100003130103'82'3''1'737389561573826213403221106722006'1'140000-6'1'163117.394239118021'1'5331'1'169.000000213.750000648.588189803.050535696.905247615.1567120-97373815738262134032251616.620234.571429...472.898038248.4026352290.250487484.001102237.0776242222.339102464.3469362'1 Adequate''-5''2000-2009''1 Single Family''2 2BR''1 Owner''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''3 150-200% Poverty''2 50.1 - 100% FMR''2 50.1 - 100% FMR''2 50.1 - 100% FMR''2 50.1 - 100% FMR''1 LTE 50% FMR''2 30 - 50% AMI''2 30 - 50% AMI''2 30 - 50% AMI''2 30 - 50% AMI''2 30 - 50% AMI''.''2 30% to 50%''-5''-5'
1'100006110249'50'5''3'5584611001716528604457442421841980'1'1130000-6'1'162150.7255444122961'1'4871'1'245.33333358.3333331167.6407811669.6434051324.6712181058.988479123000-95584617165286044574455846.019911.400000...4120.4246563103.0940636275.7689994151.785764365.3884684174.909320396.2716802'1 Adequate''-5''1980-1989''1 Single Family''4 4BR+''1 Owner''3 150-200% Poverty''4 200%+ Poverty''4 200%+ Poverty''3 150-200% Poverty''4 200%+ Poverty''3 GT FMR''3 GT FMR''3 GT FMR''2 50.1 - 100% FMR''3 GT FMR''4 60 - 80% AMI''4 60 - 80% AMI''6 100 - 120% AMI''4 60 - 80% AMI''7 120% AMI +''.''1 Less than 30%''-5''-5'
2'100006370140'53'5''3'5584611001375022897366141547041985'1'1150000-6'1'172213.789404227974'1'14051'1'159.00000037.5000001193.3932091772.6270061374.5821751068.02516828000-95584613750228973661444676.819937.500000...4124.9620163109.4529056458.3392394161.147910365.9464494276.153890497.0931972'1 Adequate''-5''1980-1989''1 Single Family''4 4BR+''1 Owner''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''3 150-200% Poverty''3 GT FMR''3 GT FMR''3 GT FMR''2 50.1 - 100% FMR''2 50.1 - 100% FMR''4 60 - 80% AMI''5 80 - 100% AMI''6 100 - 120% AMI''4 60 - 80% AMI''4 60 - 80% AMI''.''3 50% or More''-5''-5'
3'100006520140'67'5''3'558469491375022897366141396431985'1'1200000-6'1'162364.585097232220'1'2791'1'179.00000070.6666671578.8576122351.1693411820.4429001411.7002240-95584613750228973661444676.817875.000000...4191.8274923161.9267097673.4945124247.752301397.2248015404.3827634148.7566103'1 Adequate''-5''1980-1989''1 Single Family''3 3BR''1 Owner''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''4 200%+ Poverty''3 GT FMR''3 GT FMR''3 GT FMR''3 GT FMR''2 50.1 - 100% FMR''6 100 - 120% AMI''7 120% AMI +''7 120% AMI +''5 80 - 100% AMI''4 60 - 80% AMI''.''1 Less than 30%''-5''-5'
4'100007130148'26'1''3'609917371480124628394211549221980'1'1-6-6'2'10042314.524902296874'1'7595'2'146.00000012.500000759.000000759.000000759.000000759.0000009690006099114801246283942148792.816651.125000...3102.985075355.3087073195.9721153102.985075355.3087073195.9721153102.9850753'1 Adequate''Central City''1980-1989''5 50+ units''2 2BR''2 Renter''3 150-200% Poverty''3 150-200% Poverty''3 150-200% Poverty''3 150-200% Poverty''4 200%+ Poverty''3 GT FMR''3 GT FMR''3 GT FMR''3 GT FMR''3 GT FMR''3 50 - 60% AMI''3 50 - 60% AMI''3 50 - 60% AMI''3 50 - 60% AMI''7 120% AMI +''0 Not Assisted''1 Less than 30%''-5''-5'
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5 rows × 99 columns

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" + ], + "text/plain": [ + " CONTROL AGE1 METRO3 ... FMTBURDEN FMTREGION FMTSTATUS\n", + "0 '100003130103' 82 '3' ... '2 30% to 50%' '-5' '-5'\n", + "1 '100006110249' 50 '5' ... '1 Less than 30%' '-5' '-5'\n", + "2 '100006370140' 53 '5' ... '3 50% or More' '-5' '-5'\n", + "3 '100006520140' 67 '5' ... '1 Less than 30%' '-5' '-5'\n", + "4 '100007130148' 26 '1' ... '1 Less than 30%' '-5' '-5'\n", + "\n", + "[5 rows x 99 columns]" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 1 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "O5zrMTud2qFU", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 221 + }, + "outputId": "1c657ca2-f846-4949-9078-a38b0548d2fc" + }, + "source": [ + "# Look at datatypes\n", + "# a lot of object datatypes even though they seem to be strings of numbers.\n", + "national.dtypes" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "CONTROL object\n", + "AGE1 int64\n", + "METRO3 object\n", + "REGION object\n", + "LMED int64\n", + " ... \n", + "FMTINCRELAMICAT object\n", + "FMTASSISTED object\n", + "FMTBURDEN object\n", + "FMTREGION object\n", + "FMTSTATUS object\n", + "Length: 99, dtype: object" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 2 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "yIrOjVmd2yLz", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "78d50c79-114f-4010-bb0f-991b399adad3" + }, + "source": [ + "# check for null values\n", + "national.isnull().sum().any()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "False" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 3 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "2u9tdmwX3KL_", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "9a31aa94-c6f6-47c5-bbeb-d8d852d419bd" + }, + "source": [ + "# check for number of categorical vs numeric columns\n", + "cat_cols = national.columns[national.dtypes=='object']\n", + "num_cols = national.columns[national.dtypes!='object']\n", + "\n", + "print(f'{len(cat_cols)} categorical columns')\n", + "print(f'{len(num_cols)} numerical columns')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "32 categorical columns\n", + "67 numerical columns\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "UMHOtOs_3gcL", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 221 + }, + "outputId": "1afd59aa-116b-4835-ca5f-9c030164c008" + }, + "source": [ + "# We're making a copy of our data in case we mess something up.\n", + "national_processed = national.copy()\n", + "\n", + "# Categorically Encode our Variables:\n", + "# They need to all be numeric before we do PCA.\n", + "# https://pbpython.com/categorical-encoding.html\n", + "\n", + "# Cast categorical columns to \"category\" data type\n", + "national_processed[cat_cols] = national_processed[cat_cols].astype('category')\n", + "\n", + "national_processed.dtypes" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "CONTROL category\n", + "AGE1 int64\n", + "METRO3 category\n", + "REGION category\n", + "LMED int64\n", + " ... \n", + "FMTINCRELAMICAT category\n", + "FMTASSISTED category\n", + "FMTBURDEN category\n", + "FMTREGION category\n", + "FMTSTATUS category\n", + "Length: 99, dtype: object" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 5 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "ymxU-aPtQ1eq", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "outputId": "02fe0fad-81bb-404c-a4cd-92242cfe4c6c" + }, + "source": [ + "# Replace all category cell values with their numeric category codes\n", + "for col in cat_cols:\n", + " national_processed[col] = national_processed[col].cat.codes\n", + "\n", + "print(national_processed.shape)\n", + "national_processed.head()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(64535, 99)\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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5 rows × 99 columns

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" + ], + "text/plain": [ + " CONTROL AGE1 METRO3 REGION ... FMTASSISTED FMTBURDEN FMTREGION FMTSTATUS\n", + "0 0 82 2 0 ... 0 2 0 0\n", + "1 1 50 4 2 ... 0 1 0 0\n", + "2 2 53 4 2 ... 0 3 0 0\n", + "3 3 67 4 2 ... 0 1 0 0\n", + "4 4 26 0 2 ... 1 1 0 0\n", + "\n", + "[5 rows x 99 columns]" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 7 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "6NS5AQpcQ8Je", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "outputId": "3cbe9b8e-05e4-4126-f072-030c8d2ac7b4" + }, + "source": [ + "# Now we only ahve numeric columns (ints and floats)\n", + "national_processed.dtypes" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "CONTROL int32\n", + "AGE1 int64\n", + "METRO3 int8\n", + "REGION int8\n", + "LMED int64\n", + "FMR int64\n", + "L30 int64\n", + "L50 int64\n", + "L80 int64\n", + "IPOV int64\n", + "BEDRMS int64\n", + "BUILT int64\n", + "STATUS int8\n", + "TYPE int64\n", + "VALUE int64\n", + "VACANCY int64\n", + "TENURE int8\n", + "NUNITS int64\n", + "ROOMS int64\n", + "WEIGHT float64\n", + "PER int64\n", + "ZINC2 int64\n", + "ZADEQ int8\n", + "ZSMHC int64\n", + "STRUCTURETYPE int64\n", + "OWNRENT int8\n", + "UTILITY float64\n", + "OTHERCOST float64\n", + "COST06 float64\n", + "COST12 float64\n", + " ... \n", + "COSTMedRELAMICAT int64\n", + "COSTMedRELPOVPCT float64\n", + "COSTMedRELPOVCAT int64\n", + "COSTMedRELFMRPCT float64\n", + "COSTMedRELFMRCAT int64\n", + "FMTZADEQ int8\n", + "FMTMETRO3 int8\n", + "FMTBUILT int8\n", + "FMTSTRUCTURETYPE int8\n", + "FMTBEDRMS int8\n", + "FMTOWNRENT int8\n", + "FMTCOST06RELPOVCAT int8\n", + "FMTCOST08RELPOVCAT int8\n", + "FMTCOST12RELPOVCAT int8\n", + "FMTCOSTMEDRELPOVCAT int8\n", + "FMTINCRELPOVCAT int8\n", + "FMTCOST06RELFMRCAT int8\n", + "FMTCOST08RELFMRCAT int8\n", + "FMTCOST12RELFMRCAT int8\n", + "FMTCOSTMEDRELFMRCAT int8\n", + "FMTINCRELFMRCAT int8\n", + "FMTCOST06RELAMICAT int8\n", + "FMTCOST08RELAMICAT int8\n", + "FMTCOST12RELAMICAT int8\n", + "FMTCOSTMEDRELAMICAT int8\n", + "FMTINCRELAMICAT int8\n", + "FMTASSISTED int8\n", + "FMTBURDEN int8\n", + "FMTREGION int8\n", + "FMTSTATUS int8\n", + "Length: 99, dtype: object" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 10 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "WAJ8bjVcEwhA", + "colab_type": "code", + "colab": {} + }, + "source": [ + "### Your Code Here" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RQx7UvsucIrL", + "colab_type": "text" + }, + "source": [ + "# Stretch Goals\n", + "\n", + "## 1) Perform further data exploration on the HADS national dataset (the version before we one-hot encoded it) Make scatterplots and see if you can see any resemblance between the original scatterplots and the plot of the principal components that you made in 7.1. \n", + "\n", + "(You may or may not not see very much resemblance depending on the variables you choose, and that's ok!)\n", + "\n", + "## 2) Study \"Scree Plots\" and then try and make one for your PCA dataset. How many principal conponents do you need to retain in order for your PCs to contain 90% of the explained variance? \n", + "\n", + "We will present this topic formally at the beginning of tomorrow's lecture, so if you figure this stretch goal out, you're ahead of the game. \n", + "\n", + "## 3) Explore further the intuition behind eigenvalues and eigenvectors by creating your very own eigenfaces:\n", + "\n", + "Prioritize self-study over this stretch goal if you are not semi-comfortable with the topics of PCA, Eigenvalues, and Eigenvectors.\n", + "\n", + "![Eigenfaces](https://i.pinimg.com/236x/1c/f1/01/1cf101a9859437a5d096a04b05be06b4--faces-tattoo.jpg)\n", + "\n", + "You don't necessarily have to use this resource, but this will get you started: \n", + "[Eigenface Tutorial](https://sandipanweb.wordpress.com/2018/01/06/eigenfaces-and-a-simple-face-detector-with-pca-svd-in-python/)" + ] + } + ] +} diff --git a/module4-clustering/LS_DS_134_Clustering_Assignment.ipynb b/module4-clustering/LS_DS_134_Clustering_Assignment.ipynb index 3342efb0..409b2937 100644 --- a/module4-clustering/LS_DS_134_Clustering_Assignment.ipynb +++ b/module4-clustering/LS_DS_134_Clustering_Assignment.ipynb @@ -54,11 +54,11 @@ "metadata": { "id": "ws5R9X6hLJQ2", "colab_type": "code", - "outputId": "078a0dfa-1b57-4a70-b7dd-6747910059c9", "colab": { "base_uri": "https://localhost:8080/", - "height": 278 - } + "height": 258 + }, + "outputId": "3de26038-4ae4-4bf8-8bbb-0b66d1fad0c5" }, "source": [ "import pandas as pd\n", @@ -72,7 +72,7 @@ "print(df.shape)\n", "df.head()" ], - "execution_count": 0, + "execution_count": 84, "outputs": [ { "output_type": "stream", @@ -113,7 +113,19 @@ " compactness_mean\n", " concavity_mean\n", " concave points_mean\n", - " ...\n", + " symmetry_mean\n", + " fractal_dimension_mean\n", + " radius_se\n", + " texture_se\n", + " perimeter_se\n", + " area_se\n", + " smoothness_se\n", + " compactness_se\n", + " concavity_se\n", + " concave points_se\n", + " symmetry_se\n", + " fractal_dimension_se\n", + " radius_worst\n", " texture_worst\n", " perimeter_worst\n", " area_worst\n", @@ -139,7 +151,19 @@ " 0.27760\n", " 0.3001\n", " 0.14710\n", - " ...\n", + " 0.2419\n", + " 0.07871\n", + " 1.0950\n", + " 0.9053\n", + " 8.589\n", + " 153.40\n", + " 0.006399\n", + " 0.04904\n", + " 0.05373\n", + " 0.01587\n", + " 0.03003\n", + " 0.006193\n", + " 25.38\n", " 17.33\n", " 184.60\n", " 2019.0\n", @@ -163,7 +187,19 @@ " 0.07864\n", " 0.0869\n", " 0.07017\n", - " ...\n", + " 0.1812\n", + " 0.05667\n", + " 0.5435\n", + " 0.7339\n", + " 3.398\n", + " 74.08\n", + " 0.005225\n", + " 0.01308\n", + " 0.01860\n", + " 0.01340\n", + " 0.01389\n", + " 0.003532\n", + " 24.99\n", " 23.41\n", " 158.80\n", " 1956.0\n", @@ -187,7 +223,19 @@ " 0.15990\n", " 0.1974\n", " 0.12790\n", - " ...\n", + " 0.2069\n", + " 0.05999\n", + " 0.7456\n", + " 0.7869\n", + " 4.585\n", + " 94.03\n", + " 0.006150\n", + " 0.04006\n", + " 0.03832\n", + " 0.02058\n", + " 0.02250\n", + " 0.004571\n", + " 23.57\n", " 25.53\n", " 152.50\n", " 1709.0\n", @@ -211,7 +259,19 @@ " 0.28390\n", " 0.2414\n", " 0.10520\n", - " ...\n", + " 0.2597\n", + " 0.09744\n", + " 0.4956\n", + " 1.1560\n", + " 3.445\n", + " 27.23\n", + " 0.009110\n", + " 0.07458\n", + " 0.05661\n", + " 0.01867\n", + " 0.05963\n", + " 0.009208\n", + " 14.91\n", " 26.50\n", " 98.87\n", " 567.7\n", @@ -235,7 +295,19 @@ " 0.13280\n", " 0.1980\n", " 0.10430\n", - " ...\n", + " 0.1809\n", + " 0.05883\n", + " 0.7572\n", + " 0.7813\n", + " 5.438\n", + " 94.44\n", + " 0.011490\n", + " 0.02461\n", + " 0.05688\n", + " 0.01885\n", + " 0.01756\n", + " 0.005115\n", + " 22.54\n", " 16.67\n", " 152.20\n", " 1575.0\n", @@ -249,44 +321,15 @@ " \n", " \n", "\n", - "

5 rows × 33 columns

\n", "" ], "text/plain": [ - " id diagnosis radius_mean texture_mean perimeter_mean area_mean \\\n", - "0 842302 M 17.99 10.38 122.80 1001.0 \n", - "1 842517 M 20.57 17.77 132.90 1326.0 \n", - "2 84300903 M 19.69 21.25 130.00 1203.0 \n", - "3 84348301 M 11.42 20.38 77.58 386.1 \n", - "4 84358402 M 20.29 14.34 135.10 1297.0 \n", - "\n", - " smoothness_mean compactness_mean concavity_mean concave points_mean \\\n", - "0 0.11840 0.27760 0.3001 0.14710 \n", - "1 0.08474 0.07864 0.0869 0.07017 \n", - "2 0.10960 0.15990 0.1974 0.12790 \n", - "3 0.14250 0.28390 0.2414 0.10520 \n", - "4 0.10030 0.13280 0.1980 0.10430 \n", - "\n", - " ... texture_worst perimeter_worst area_worst smoothness_worst \\\n", - "0 ... 17.33 184.60 2019.0 0.1622 \n", - "1 ... 23.41 158.80 1956.0 0.1238 \n", - "2 ... 25.53 152.50 1709.0 0.1444 \n", - "3 ... 26.50 98.87 567.7 0.2098 \n", - "4 ... 16.67 152.20 1575.0 0.1374 \n", - "\n", - " compactness_worst concavity_worst concave points_worst symmetry_worst \\\n", - "0 0.6656 0.7119 0.2654 0.4601 \n", - "1 0.1866 0.2416 0.1860 0.2750 \n", - "2 0.4245 0.4504 0.2430 0.3613 \n", - "3 0.8663 0.6869 0.2575 0.6638 \n", - "4 0.2050 0.4000 0.1625 0.2364 \n", - "\n", - " fractal_dimension_worst Unnamed: 32 \n", - "0 0.11890 NaN \n", - "1 0.08902 NaN \n", - "2 0.08758 NaN \n", - "3 0.17300 NaN \n", - "4 0.07678 NaN \n", + " id diagnosis ... fractal_dimension_worst Unnamed: 32\n", + "0 842302 M ... 0.11890 NaN\n", + "1 842517 M ... 0.08902 NaN\n", + "2 84300903 M ... 0.08758 NaN\n", + "3 84348301 M ... 0.17300 NaN\n", + "4 84358402 M ... 0.07678 NaN\n", "\n", "[5 rows x 33 columns]" ] @@ -294,7 +337,7 @@ "metadata": { "tags": [] }, - "execution_count": 1 + "execution_count": 84 } ] }, @@ -313,19 +356,95 @@ { "cell_type": "code", "metadata": { - "id": "86MHoPJon_aC", + "id": "t7opdFbCvv3B", + "colab_type": "code", + "colab": {} + }, + "source": [ + "df_primary = df.copy()" + ], + "execution_count": 12, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "4SbusZ4ayGaF", "colab_type": "code", - "outputId": "d4d9f1cd-c63c-4623-954e-11a61d1e3ced", "colab": { "base_uri": "https://localhost:8080/", - "height": 261 + "height": 595 + }, + "outputId": "e6a0e09a-a68f-4f1d-c66e-04469b836504" + }, + "source": [ + "df.isnull().sum()" + ], + "execution_count": 13, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "id 0\n", + "diagnosis 0\n", + "radius_mean 0\n", + "texture_mean 0\n", + "perimeter_mean 0\n", + "area_mean 0\n", + "smoothness_mean 0\n", + "compactness_mean 0\n", + "concavity_mean 0\n", + "concave points_mean 0\n", + "symmetry_mean 0\n", + "fractal_dimension_mean 0\n", + "radius_se 0\n", + "texture_se 0\n", + "perimeter_se 0\n", + "area_se 0\n", + "smoothness_se 0\n", + "compactness_se 0\n", + "concavity_se 0\n", + "concave points_se 0\n", + "symmetry_se 0\n", + "fractal_dimension_se 0\n", + "radius_worst 0\n", + "texture_worst 0\n", + "perimeter_worst 0\n", + "area_worst 0\n", + "smoothness_worst 0\n", + "compactness_worst 0\n", + "concavity_worst 0\n", + "concave points_worst 0\n", + "symmetry_worst 0\n", + "fractal_dimension_worst 0\n", + "Unnamed: 32 569\n", + "dtype: int64" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 13 } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "86MHoPJon_aC", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 241 + }, + "outputId": "91b2726f-2504-416a-f487-b10d4613ed2c" }, "source": [ - "df = df.drop('diagnosis', axis=1)\n", + "df = df.drop(['id','diagnosis', 'Unnamed: 32'], axis=1)\n", "df.head()" ], - "execution_count": 0, + "execution_count": 14, "outputs": [ { "output_type": "execute_result", @@ -349,7 +468,6 @@ " \n", " \n", " \n", - " id\n", " radius_mean\n", " texture_mean\n", " perimeter_mean\n", @@ -359,7 +477,18 @@ " concavity_mean\n", " concave points_mean\n", " symmetry_mean\n", - " ...\n", + " fractal_dimension_mean\n", + " radius_se\n", + " texture_se\n", + " perimeter_se\n", + " area_se\n", + " smoothness_se\n", + " compactness_se\n", + " concavity_se\n", + " concave points_se\n", + " symmetry_se\n", + " fractal_dimension_se\n", + " radius_worst\n", " texture_worst\n", " perimeter_worst\n", " area_worst\n", @@ -369,13 +498,11 @@ " concave points_worst\n", " symmetry_worst\n", " fractal_dimension_worst\n", - " Unnamed: 32\n", " \n", " \n", " \n", " \n", " 0\n", - " 842302\n", " 17.99\n", " 10.38\n", " 122.80\n", @@ -385,7 +512,18 @@ " 0.3001\n", " 0.14710\n", " 0.2419\n", - " ...\n", + " 0.07871\n", + " 1.0950\n", + " 0.9053\n", + " 8.589\n", + " 153.40\n", + " 0.006399\n", + " 0.04904\n", + " 0.05373\n", + " 0.01587\n", + " 0.03003\n", + " 0.006193\n", + " 25.38\n", " 17.33\n", " 184.60\n", " 2019.0\n", @@ -395,11 +533,9 @@ " 0.2654\n", " 0.4601\n", " 0.11890\n", - " NaN\n", " \n", " \n", " 1\n", - " 842517\n", " 20.57\n", " 17.77\n", " 132.90\n", @@ -409,7 +545,18 @@ " 0.0869\n", " 0.07017\n", " 0.1812\n", - " ...\n", + " 0.05667\n", + " 0.5435\n", + " 0.7339\n", + " 3.398\n", + " 74.08\n", + " 0.005225\n", + " 0.01308\n", + " 0.01860\n", + " 0.01340\n", + " 0.01389\n", + " 0.003532\n", + " 24.99\n", " 23.41\n", " 158.80\n", " 1956.0\n", @@ -419,11 +566,9 @@ " 0.1860\n", " 0.2750\n", " 0.08902\n", - " NaN\n", " \n", " \n", " 2\n", - " 84300903\n", " 19.69\n", " 21.25\n", " 130.00\n", @@ -433,7 +578,18 @@ " 0.1974\n", " 0.12790\n", " 0.2069\n", - " ...\n", + " 0.05999\n", + " 0.7456\n", + " 0.7869\n", + " 4.585\n", + " 94.03\n", + " 0.006150\n", + " 0.04006\n", + " 0.03832\n", + " 0.02058\n", + " 0.02250\n", + " 0.004571\n", + " 23.57\n", " 25.53\n", " 152.50\n", " 1709.0\n", @@ -443,11 +599,9 @@ " 0.2430\n", " 0.3613\n", " 0.08758\n", - " NaN\n", " \n", " \n", " 3\n", - " 84348301\n", " 11.42\n", " 20.38\n", " 77.58\n", @@ -457,7 +611,18 @@ " 0.2414\n", " 0.10520\n", " 0.2597\n", - " ...\n", + " 0.09744\n", + " 0.4956\n", + " 1.1560\n", + " 3.445\n", + " 27.23\n", + " 0.009110\n", + " 0.07458\n", + " 0.05661\n", + " 0.01867\n", + " 0.05963\n", + " 0.009208\n", + " 14.91\n", " 26.50\n", " 98.87\n", " 567.7\n", @@ -467,11 +632,9 @@ " 0.2575\n", " 0.6638\n", " 0.17300\n", - " NaN\n", " \n", " \n", " 4\n", - " 84358402\n", " 20.29\n", " 14.34\n", " 135.10\n", @@ -481,7 +644,18 @@ " 0.1980\n", " 0.10430\n", " 0.1809\n", - " ...\n", + " 0.05883\n", + " 0.7572\n", + " 0.7813\n", + " 5.438\n", + " 94.44\n", + " 0.011490\n", + " 0.02461\n", + " 0.05688\n", + " 0.01885\n", + " 0.01756\n", + " 0.005115\n", + " 22.54\n", " 16.67\n", " 152.20\n", " 1575.0\n", @@ -491,56 +665,26 @@ " 0.1625\n", " 0.2364\n", " 0.07678\n", - " NaN\n", " \n", " \n", "\n", - "

5 rows × 32 columns

\n", "" ], "text/plain": [ - " id radius_mean texture_mean perimeter_mean area_mean \\\n", - "0 842302 17.99 10.38 122.80 1001.0 \n", - "1 842517 20.57 17.77 132.90 1326.0 \n", - "2 84300903 19.69 21.25 130.00 1203.0 \n", - "3 84348301 11.42 20.38 77.58 386.1 \n", - "4 84358402 20.29 14.34 135.10 1297.0 \n", - "\n", - " smoothness_mean compactness_mean concavity_mean concave points_mean \\\n", - "0 0.11840 0.27760 0.3001 0.14710 \n", - "1 0.08474 0.07864 0.0869 0.07017 \n", - "2 0.10960 0.15990 0.1974 0.12790 \n", - "3 0.14250 0.28390 0.2414 0.10520 \n", - "4 0.10030 0.13280 0.1980 0.10430 \n", + " radius_mean texture_mean ... symmetry_worst fractal_dimension_worst\n", + "0 17.99 10.38 ... 0.4601 0.11890\n", + "1 20.57 17.77 ... 0.2750 0.08902\n", + "2 19.69 21.25 ... 0.3613 0.08758\n", + "3 11.42 20.38 ... 0.6638 0.17300\n", + "4 20.29 14.34 ... 0.2364 0.07678\n", "\n", - " symmetry_mean ... texture_worst perimeter_worst area_worst \\\n", - "0 0.2419 ... 17.33 184.60 2019.0 \n", - "1 0.1812 ... 23.41 158.80 1956.0 \n", - "2 0.2069 ... 25.53 152.50 1709.0 \n", - "3 0.2597 ... 26.50 98.87 567.7 \n", - "4 0.1809 ... 16.67 152.20 1575.0 \n", - "\n", - " smoothness_worst compactness_worst concavity_worst concave points_worst \\\n", - "0 0.1622 0.6656 0.7119 0.2654 \n", - "1 0.1238 0.1866 0.2416 0.1860 \n", - "2 0.1444 0.4245 0.4504 0.2430 \n", - "3 0.2098 0.8663 0.6869 0.2575 \n", - "4 0.1374 0.2050 0.4000 0.1625 \n", - "\n", - " symmetry_worst fractal_dimension_worst Unnamed: 32 \n", - "0 0.4601 0.11890 NaN \n", - "1 0.2750 0.08902 NaN \n", - "2 0.3613 0.08758 NaN \n", - "3 0.6638 0.17300 NaN \n", - "4 0.2364 0.07678 NaN \n", - "\n", - "[5 rows x 32 columns]" + "[5 rows x 30 columns]" ] }, "metadata": { "tags": [] }, - "execution_count": 2 + "execution_count": 14 } ] }, @@ -562,70 +706,1239 @@ "metadata": { "id": "U92Y3jNKPpjJ", "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 731 + }, + "outputId": "2c99cda2-20a0-495a-90fd-b8cb59ad7a2a" + }, + "source": [ + "# Perform K-Means Clustering on the Dataset\n", + "print(df.shape)\n", + "print(df.dtypes)\n", + "df.columns" + ], + "execution_count": 15, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(569, 30)\n", + "radius_mean float64\n", + "texture_mean float64\n", + "perimeter_mean float64\n", + "area_mean float64\n", + "smoothness_mean float64\n", + "compactness_mean float64\n", + "concavity_mean float64\n", + "concave points_mean float64\n", + "symmetry_mean float64\n", + "fractal_dimension_mean float64\n", + "radius_se float64\n", + "texture_se float64\n", + "perimeter_se float64\n", + "area_se float64\n", + "smoothness_se float64\n", + "compactness_se float64\n", + "concavity_se float64\n", + "concave points_se float64\n", + "symmetry_se float64\n", + "fractal_dimension_se float64\n", + "radius_worst float64\n", + "texture_worst float64\n", + "perimeter_worst float64\n", + "area_worst float64\n", + "smoothness_worst float64\n", + "compactness_worst float64\n", + "concavity_worst float64\n", + "concave points_worst float64\n", + "symmetry_worst float64\n", + "fractal_dimension_worst float64\n", + "dtype: object\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Index(['radius_mean', 'texture_mean', 'perimeter_mean', 'area_mean',\n", + " 'smoothness_mean', 'compactness_mean', 'concavity_mean',\n", + " 'concave points_mean', 'symmetry_mean', 'fractal_dimension_mean',\n", + " 'radius_se', 'texture_se', 'perimeter_se', 'area_se', 'smoothness_se',\n", + " 'compactness_se', 'concavity_se', 'concave points_se', 'symmetry_se',\n", + " 'fractal_dimension_se', 'radius_worst', 'texture_worst',\n", + " 'perimeter_worst', 'area_worst', 'smoothness_worst',\n", + " 'compactness_worst', 'concavity_worst', 'concave points_worst',\n", + " 'symmetry_worst', 'fractal_dimension_worst'],\n", + " dtype='object')" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 15 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "wZiN-zEKmtEt", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 102 + }, + "outputId": "5c5c15aa-764b-43e6-8133-e896e56eb6f2" + }, + "source": [ + "print(df[df[:]>100].count().sum())\n", + "print(df[(df[:]<100) & (df[:]>1)].count().sum())\n", + "print(df[(df[:]<1) & (df[:]>.1)].count().sum())\n", + "print(df[(df[:]<.1) & (df[:]>.01)].count().sum())\n", + "print(df[df[:]<.01].count().sum())" + ], + "execution_count": 16, + "outputs": [ + { + "output_type": "stream", + "text": [ + "1610\n", + "4440\n", + "4507\n", + "4938\n", + "1569\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "N1ewNIsyqHVx", + "colab_type": "code", "colab": {} }, "source": [ - "# Perform K-Means Clustering on the Dataset" + "sum_of_squared_distances = []\n", + "K = range(1,7)\n", + "for k in K:\n", + " km = KMeans(n_clusters = k)\n", + " km = km.fit(df)\n", + " sum_of_squared_distances.append(km.inertia_)" ], - "execution_count": 0, + "execution_count": 17, "outputs": [] }, { - "cell_type": "markdown", + "cell_type": "code", "metadata": { - "id": "7ghqYSxrP_FE", - "colab_type": "text" + "id": "U70OHvm6rKfb", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 295 + }, + "outputId": "ad0f8ee9-38db-420c-832b-eba4a2355869" }, "source": [ - "## Check you work: \n", - "\n", - "This is something that in a truly unsupervised learning situation **WOULD NOT BE POSSIBLE**. But for educational purposes go back and grab the true diagnosis column (label) from the original dataset. Take your cluster labels and compare them to the original diagnosis column. You can make scatterplots for each to see how they compare or you can calculate a percent accuracy score like: \n", - "\\begin{align}\n", - "\\frac{\\text{Num Correct Labels}}{\\text{Num Total Observations}}\n", - "\\end{align}" + "plt.plot(K, sum_of_squared_distances, 'bx-')\n", + "plt.xlabel('k')\n", + "plt.ylabel('Sum_of_squared_distances')\n", + "plt.title('Elbow Method For Optimal k')\n", + "plt.show()" + ], + "execution_count": 18, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "f16Qlo__spPK", + "colab_type": "code", + "colab": {} + }, + "source": [ + "k = 2\n", + "model = KMeans(n_clusters=k, max_iter=1)" + ], + "execution_count": 19, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "nQ2bGyiBtoFA", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "20ae7029-6f03-40d1-d052-5acef0ae310b" + }, + "source": [ + "model.fit(df.values)" + ], + "execution_count": 20, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=1,\n", + " n_clusters=2, n_init=10, n_jobs=None, precompute_distances='auto',\n", + " random_state=None, tol=0.0001, verbose=0)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 20 + } ] }, { "cell_type": "code", "metadata": { - "id": "OIG7-yGLP-eA", + "id": "QXn9eZqytxQb", "colab_type": "code", "colab": {} }, "source": [ - "# Your Code Here" + "df['cluster'] = model.labels_" ], - "execution_count": 0, + "execution_count": 21, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "h59qL01jvDIE", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "b1121760-08ae-4974-99f3-046396d9d4ed" + }, + "source": [ + "# what's our silhouette score?\n", + "from sklearn import metrics \n", + "metrics.silhouette_score(df, model.labels_, metric='euclidean')" + ], + "execution_count": 22, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0.6972647834018775" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 22 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "yIXA07ytvGsK", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 476 + }, + "outputId": "342e92b6-f636-463c-b8ba-a021f71883a6" + }, + "source": [ + "model.labels_" + ], + "execution_count": 23, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1,\n", + " 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1,\n", + " 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0,\n", + " 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1,\n", + " 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,\n", + " 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1,\n", + " 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1,\n", + " 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1,\n", + " 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1,\n", + " 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,\n", + " 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1],\n", + " dtype=int32)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 23 + } + ] + }, { "cell_type": "markdown", "metadata": { - "id": "BedOTS0eJ9_K", + "id": "7ghqYSxrP_FE", "colab_type": "text" }, "source": [ - "# 2) Perform PCA on your dataset first and *then* use k-means clustering. \n", + "## Check you work: \n", "\n", - "- You need to standardize your data before PCA.\n", - "- First try clustering just on PC1 and PC2 so that you can make a scatterplot of your clustering.\n", - "- Then use use a scree plot to decide how many principal components to include in your clustering, and use however many principal components you need in order to retain 90% of the variation of the original dataset\n", - "\n" + "This is something that in a truly unsupervised learning situation **WOULD NOT BE POSSIBLE**. But for educational purposes go back and grab the true diagnosis column (label) from the original dataset. Take your cluster labels and compare them to the original diagnosis column. You can make scatterplots for each to see how they compare or you can calculate a percent accuracy score like: \n", + "\\begin{align}\n", + "\\frac{\\text{Num Correct Labels}}{\\text{Num Total Observations}}\n", + "\\end{align}" ] }, { "cell_type": "code", "metadata": { - "id": "dW1AeAK8PNah", + "id": "Ia7QCIPv2tHR", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "e3704206-49b8-49b8-9cd8-945f5f859b2b" + }, + "source": [ + "df_primary['diagnosis'].value_counts()" + ], + "execution_count": 24, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "B 357\n", + "M 212\n", + "Name: diagnosis, dtype: int64" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 24 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "86E_8xDZ3SXs", "colab_type": "code", "colab": {} }, "source": [ - "##### Your Code Here #####" + "df_primary['diagnosis_num'] = np.where(df_primary['diagnosis'] == 'B', 1, 0)" ], - "execution_count": 0, + "execution_count": 25, "outputs": [] }, + { + "cell_type": "code", + "metadata": { + "id": "iXLb2k2s3p6b", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 459 + }, + "outputId": "4aa8b522-5814-4406-db59-73f8f6e8ca54" + }, + "source": [ + "correct_labels = np.array(df_primary['diagnosis_num'])\n", + "correct_labels" + ], + "execution_count": 26, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0,\n", + " 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0,\n", + " 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0,\n", + " 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1,\n", + " 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0,\n", + " 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0,\n", + " 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1,\n", + " 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0,\n", + " 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0,\n", + " 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0,\n", + " 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1,\n", + " 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1,\n", + " 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,\n", + " 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,\n", + " 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1,\n", + " 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 26 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "3usnkyx04i0G", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "915476d3-99d2-4512-916c-33e0da0954c2" + }, + "source": [ + "compare = model.labels_== correct_labels\n", + "compare[compare ==True].sum()" + ], + "execution_count": 27, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "486" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 27 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "8-kNELJHAet1", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "980aeb48-9b99-4897-83ee-30f1ac5efce9" + }, + "source": [ + "83/569" + ], + "execution_count": 28, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0.14586994727592267" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 28 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BedOTS0eJ9_K", + "colab_type": "text" + }, + "source": [ + "# 2) Perform PCA on your dataset first and *then* use k-means clustering. \n", + "\n", + "- You need to standardize your data before PCA.\n", + "- First try clustering just on PC1 and PC2 so that you can make a scatterplot of your clustering.\n", + "- Then use use a scree plot to decide how many principal components to include in your clustering, and use however many principal components you need in order to retain 90% of the variation of the original dataset\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "dW1AeAK8PNah", + "colab_type": "code", + "colab": {} + }, + "source": [ + "##### Your Code Here #####" + ], + "execution_count": 29, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "uDTwE9NpGRHw", + "colab_type": "code", + "colab": {} + }, + "source": [ + "# read in data without column indexes\n", + "df_pca = pd.read_csv(\"https://raw.githubusercontent.com/ryanleeallred/datasets/master/Cancer_Cells.csv\", index_col=0)" + ], + "execution_count": 38, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "av0foH-EPF8m", + "colab_type": "code", + "colab": {} + }, + "source": [ + "df_pca = df_pca.drop(['diagnosis', 'Unnamed: 32'], axis=1)" + ], + "execution_count": 39, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "6HXkLjApBK7V", + "colab_type": "code", + "colab": {} + }, + "source": [ + "# scale data\n", + "scaler = StandardScaler()\n", + "df_pca_scaled = scaler.fit_transform(df_pca)" + ], + "execution_count": 40, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "lOTe_pK5Hon4", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "da6a8da3-6baa-472b-d060-467f5dab3fbc" + }, + "source": [ + "# turn data back into a dataframe\n", + "df_pca_scaled = pd.DataFrame(df_pca_scaled)\n", + "df_pca_scaled.shape" + ], + "execution_count": 41, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(569, 30)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 41 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "NaHbd5X7J93_", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 544 + }, + "outputId": "9d3deed8-519e-4b48-986b-9ca24fd8e8cf" + }, + "source": [ + "# did that work?\n", + "df_pca_scaled.mean()" + ], + "execution_count": 42, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0 -1.256562e-16\n", + "1 1.049736e-16\n", + "2 -1.272171e-16\n", + "3 -1.900452e-16\n", + "4 1.490704e-16\n", + "5 2.544342e-16\n", + "6 -1.338511e-16\n", + "7 -8.429110e-17\n", + "8 2.081912e-16\n", + "9 5.408679e-16\n", + "10 2.475807e-16\n", + "11 -9.912009e-17\n", + "12 -2.968237e-16\n", + "13 -1.088760e-16\n", + "14 4.426014e-16\n", + "15 1.958988e-16\n", + "16 1.678017e-16\n", + "17 2.185325e-17\n", + "18 1.523874e-16\n", + "19 -5.658430e-17\n", + "20 -7.988142e-16\n", + "21 -1.834112e-17\n", + "22 -4.015534e-16\n", + "23 -2.848727e-17\n", + "24 -2.189227e-16\n", + "25 -2.579464e-16\n", + "26 1.143393e-16\n", + "27 2.829215e-16\n", + "28 1.670212e-16\n", + "29 2.321908e-16\n", + "dtype: float64" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 42 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "tkSJB_lrKPfw", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 544 + }, + "outputId": "39e6f46f-bbc9-4724-a877-2681644c6ee3" + }, + "source": [ + "df_pca_scaled[:].std()" + ], + "execution_count": 43, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0 1.00088\n", + "1 1.00088\n", + "2 1.00088\n", + "3 1.00088\n", + "4 1.00088\n", + "5 1.00088\n", + "6 1.00088\n", + "7 1.00088\n", + "8 1.00088\n", + "9 1.00088\n", + "10 1.00088\n", + "11 1.00088\n", + "12 1.00088\n", + "13 1.00088\n", + "14 1.00088\n", + "15 1.00088\n", + "16 1.00088\n", + "17 1.00088\n", + "18 1.00088\n", + "19 1.00088\n", + "20 1.00088\n", + "21 1.00088\n", + "22 1.00088\n", + "23 1.00088\n", + "24 1.00088\n", + "25 1.00088\n", + "26 1.00088\n", + "27 1.00088\n", + "28 1.00088\n", + "29 1.00088\n", + "dtype: float64" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 43 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "T41e26rSBREv", + "colab_type": "code", + "colab": {} + }, + "source": [ + "# now we can apply pca\n", + "pca = PCA(n_components = 2)" + ], + "execution_count": 44, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "7NT00OqHBfVc", + "colab_type": "code", + "colab": {} + }, + "source": [ + "pca_features = pca.fit_transform(df_pca_scaled)" + ], + "execution_count": 45, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "P1KaEOlSBoQf", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "7f03abc6-1242-47d4-d5fc-72a0bf047975" + }, + "source": [ + "pca.explained_variance_ratio_" + ], + "execution_count": 46, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([0.44272026, 0.18971182])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 46 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Z2gt_ImxBq86", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "1cbb2bb2-5f66-4169-c3ed-1872d164d121" + }, + "source": [ + "# how much info are we left with?\n", + "sum(pca.explained_variance_ratio_)" + ], + "execution_count": 47, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0.6324320765155956" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 47 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Gu2dqMI_Br21", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "aa9a0e53-fb09-468a-8bd7-75e545171ad7" + }, + "source": [ + "#how much info did we lose?\n", + "1 - sum(pca.explained_variance_ratio_)" + ], + "execution_count": 48, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0.36756792348440437" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 48 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "VNvzHZh7K2C_", + "colab_type": "code", + "colab": {} + }, + "source": [ + "# turn that into a datframe\n", + "df_done_pca = pd.DataFrame(pca_features, columns=['PC1', 'PC2'])" + ], + "execution_count": 49, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "y-NlHRypLdCa", + "colab_type": "code", + "colab": {} + }, + "source": [ + "# now apply clustering\n", + "k = 3\n", + "model = KMeans(n_clusters=k, max_iter=1)" + ], + "execution_count": 66, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "UKQHGOLrOCYE", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "outputId": "14233288-ecb9-4e58-a91b-169823cd1fa1" + }, + "source": [ + "model.fit(df_done_pca)" + ], + "execution_count": 67, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=1,\n", + " n_clusters=3, n_init=10, n_jobs=None, precompute_distances='auto',\n", + " random_state=None, tol=0.0001, verbose=0)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 67 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "rrgEvacCPtjs", + "colab_type": "code", + "colab": {} + }, + "source": [ + "df_done_pca['cluster'] = model.labels_" + ], + "execution_count": 68, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "tM8BZO0SPxaG", + "colab_type": "code", + "colab": {} + }, + "source": [ + "centroids = model.cluster_centers_" + ], + "execution_count": 69, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "P_ksPeu8P1VO", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 142 + }, + "outputId": "dd5d82e6-b2c6-4cf4-c5a9-223065917cf6" + }, + "source": [ + "cc = pd.DataFrame(centroids)\n", + "cc.head()" + ], + "execution_count": 70, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " 0 1 2\n", + "0 4.119029 -2.417175 0.930435\n", + "1 -2.246583 -0.036333 0.019178\n", + "2 3.891174 3.272322 0.853933" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 70 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "WlqBkrq1P46a", + "colab_type": "code", + "colab": {} + }, + "source": [ + "# Setup some colors for plotting\n", + "base_colors = ['r', 'g', 'b']\n", + "colors = [base_colors[centroid] for centroid in model.labels_]" + ], + "execution_count": 71, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "Y2U8ktzBP97P", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + }, + "outputId": "63d872b7-0fa7-4fac-84d5-4600b3241e35" + }, + "source": [ + "fig, ax = plt.subplots(figsize=(7,6))\n", + "ax.scatter(df_done_pca['PC1'], df_done_pca['PC2'], c=colors)\n", + "ax.scatter(cc[0], cc[1], c=base_colors, s=100);" + ], + "execution_count": 72, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "JSMTrjrmmMDF", + "colab_type": "code", + "colab": {} + }, + "source": [ + "pca1 = PCA(n_components = 10)" + ], + "execution_count": 73, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "voRwcO_qmQ8s", + "colab_type": "code", + "colab": {} + }, + "source": [ + "pca_features1 = pca1.fit_transform(df_pca_scaled)" + ], + "execution_count": 74, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "rQmQr3Zsma4y", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "714545f1-6724-4989-8d3e-3bfcc32353ad" + }, + "source": [ + "pca1.explained_variance_ratio_" + ], + "execution_count": 75, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([0.44272026, 0.18971182, 0.09393163, 0.06602135, 0.05495768,\n", + " 0.04024522, 0.02250734, 0.01588724, 0.01389649, 0.01168978])" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 75 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Q2d5lCLymhwz", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "b74666e3-79ad-4961-fab1-b9d800ebf89d" + }, + "source": [ + "#how much info did we lose?\n", + "1 - sum(pca1.explained_variance_ratio_)" + ], + "execution_count": 76, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0.048431185663827536" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 76 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Nnxv1WWNmu1C", + "colab_type": "code", + "colab": {} + }, + "source": [ + "num_components=len(pca1.explained_variance_ratio_)" + ], + "execution_count": 81, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "LG6gKc01mxdA", + "colab_type": "code", + "colab": {} + }, + "source": [ + "ind = np.arange(num_components) " + ], + "execution_count": 82, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "mTk3UGf2mzdP", + "colab_type": "code", + "colab": {} + }, + "source": [ + "vals = pca1.explained_variance_ratio_" + ], + "execution_count": 83, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "2pj1clM1m4Xb", + "colab_type": "code", + "colab": {} + }, + "source": [ + "def scree_plot(pca):\n", + "\n", + " num_components=len(pca.explained_variance_ratio_)\n", + " ind = np.arange(num_components)\n", + " vals = pca.explained_variance_ratio_\n", + " \n", + " plt.figure(figsize=(18, 6))\n", + " ax = plt.subplot(111)\n", + " cumvals = np.cumsum(vals)\n", + " ax.bar(ind, vals)\n", + " ax.plot(ind, cumvals, c='r')\n", + " for i in range(num_components):\n", + " ax.annotate(r\"%s\" % ((str(vals[i]*100)[:3])), (ind[i], vals[i]), va=\"bottom\", ha=\"center\", fontsize=4.5)\n", + " \n", + " ax.xaxis.set_tick_params(width=0)\n", + " ax.yaxis.set_tick_params(width=2, length=12)\n", + "\n", + " ax.set_xlabel(\"Principal Component\")\n", + " ax.set_ylabel(\"Variance Explained (%)\")\n", + " plt.title('Explained Variance Per Principal Component')" + ], + "execution_count": 86, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "LlE1Wfdzm6FM", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 404 + }, + "outputId": "bd7b0fc0-b624-457b-8381-aa4cfc8201cf" + }, + "source": [ + "scree_plot(pca1)" + ], + "execution_count": 87, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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