Merge pull request #27 from anesh612/master

Added gradient descent

Author: cozek

algorithms/machine_learning/Gradient-Descent/data_.txt

@@ -0,0 +1,97 @@
+6.1101,17.592
+5.5277,9.1302
+8.5186,13.662
+7.0032,11.854
+5.8598,6.8233
+8.3829,11.886
+7.4764,4.3483
+8.5781,12
+6.4862,6.5987
+5.0546,3.8166
+5.7107,3.2522
+14.164,15.505
+5.734,3.1551
+8.4084,7.2258
+5.6407,0.71618
+5.3794,3.5129
+6.3654,5.3048
+5.1301,0.56077
+6.4296,3.6518
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+20.27,21.767
+5.4901,4.263
+6.3261,5.1875
+5.5649,3.0825
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+10.957,7.0467
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algorithms/machine_learning/Gradient-Descent/gradientdescent.m

@@ -0,0 +1,29 @@
+% This function demonstrates gradient descent in case of linear regression with one variable.
+
+% Theta is a column vector with two elements which this function returns after modifying it.
+
+% This function receives the feature vector x, vector of actual target variables Y, Theta
+
+% containing initial values of theta_0 and theta_1, learning rate Alpha, number of iterations
+
+% noi.
+
+function Theta = gradientdescent(x, Y, Theta, Alpha, noi)
+
+    n = length(Y); % Number of training examples. 
+
+    for i = 1:noi 
+
+        theta_1 = Theta(1) - Alpha * (1 / n) * sum(((x * Theta) - Y) .* x(:, 1)); % Temporary variable to simultaneously update theta_0 but i have used 1 to
+
+                                                                                  % avoid confusion since indexing in MATLAB/Octave starts from 1.
+
+        theta_2 = Theta(2) - Alpha * (1 / n) * sum(((x * Theta) - Y) .* x(:, 2)); % Temporary variable to simultaneously update theta_1.
+
+        Theta(1) = theta_1; % Assigning first temporary value to update first actual value simultaneously.  
+    
+        Theta(2) = theta_2; % Assigning second temporary value to update second actual value simultaneously. 
+
+    end
+
+end

algorithms/machine_learning/Gradient-Descent/runGradientDescent.m

@@ -0,0 +1,29 @@
+% This script will pass sample parameters to gradient descent function and get Theta.
+
+% I have used data consisting of populations as variables and profits as target values.
+
+% Navigate to directory where you keep these three files on octave cli and then execute.  
+
+data = load('data_.txt');
+
+Y = data(:, 2); % Y is a column vector with all entries in second column of data matrix.
+
+n = length(Y);  
+
+x = [ones(n, 1), data(:,1)]; % x is the matrix with first column as ones and second data. 
+
+Theta = zeros(2, 1); % Initial Theta vector with both theta values set to zero (column).  
+
+Alpha = 0.01; 
+
+noi = 1500;
+
+Theta = gradientdescent(x, Y, Theta, Alpha, noi);
+
+fprintf('New theta vector is below:\n');
+
+fprintf('%f\n', Theta);
+
+fprintf('Expected Theta vector (approx)\n');
+
+fprintf(' -3.6303\n 1.1664\n\n');