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PROJ1/Assignment1_ML_Yildirim_Kocoglu.m

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+% Assignment#1 - Machine Learning
+% Name: Yildirim Kocoglu
+
+% Clear and close all
+clear;
+clc;
+close all;
+
+% Load the data
+Data = xlsread('C:\Users\ykocoglu\Desktop\Classes\ML TTU\PROJ1\proj1Dataset.xlsx', 1, 'A2:B407'); % Please change the directory path (if needed)
+
+% Delete any "Nan rows" (Missing Data)
+Data(any(isnan(Data), 2), :) = [];
+
+% Seperate the Data into x (features - Weight) and y (realizations - Horsepower)
+x = Data(:,1);
+y = Data(:,2);
+
+% Plot the scatter plot of x vs y
+figure(1)
+scatter(x,y,50,'x','r','LineWidth',2);
+title('Matlab''s "carbig" dataset');
+xlabel('Weight');
+ylabel('Horsepower');
+hold on;
+%%  Analytical solution
+
+
+x = [Data(:,1), ones(size(Data,1),1)];
+
+% Analytical solution - equation
+w = pinv(x'*x)*x'*y;
+y1 = x*w;
+
+% Cost function from analytical solution
+JJ = sum((y - y1).^2);
+
+% Plot the analytical solution line on the scatter plot
+
+p = plot(x(:,1),y1, 'LineWidth',2, 'color', 'b');
+legend(p,'Closed form')
+hold off;
+
+%%  Gradient Descent solution
+
+% Set learning rate (rho) - CAN BE ADJUSTED!
+rho = 0.001;
+
+% Set Random initial guess between 0 and 1 for weights (changes at each run!)
+w2 = rand(2,1);
+
+
+% Initialize niter to keep track in the while loop
+niter = 0;
+
+% Initialize Cost function (J) to monitor
+J = zeros(niter,1);
+w_matrix = zeros(size(w2,1),niter);
+
+% Normalize the data
+xnorm = (x(:,1)-mean(x(:,1)))/std(x(:,1));
+
+% Add 1 vector to xnorm for bias
+xnorm = [xnorm,ones(size(xnorm,1),1)];
+
+% Set initial gradient_norm and tolerance in the following scale:
+% gradient_norm > tolerance (To avoid issues within the while loop) - CAN BE ADJUSTED!
+gradient_norm = 1;
+tolerance = 1*10^-1;
+
+% Set maximum number of iterations for the while loop - CAN BE ADJUSTED!
+max_iter = 10000;
+
+% GRADIENT DESCENT ALGORITHM!
+while gradient_norm > tolerance
+
+% Store the weights (w)
+w_matrix(:,niter+1) = w2;
+gradient = (2.*w2'*(xnorm'*xnorm) - 2.*y'*xnorm);
+w2 = w2 - rho.*gradient';
+
+% Store Cost function (J)
+y2 = xnorm*w2;
+J(niter+1) = sum((y - y2).^2);
+
+% Keep track of number of iterations
+niter = niter + 1;
+
+% STOPPING CRITERIA (If gradient <= tolerance or iterations >= 10000)
+
+gradient_norm = norm(gradient); % Break out of while loop if gradient_norm < tolerance
+
+if niter >= max_iter
+    fprintf('Gradient Descent could not converge within max_iter: %d \n\nTry to adjust the following parameters in the following order:\n1) rho\n2) max_iter\n3) tolerance ( < initial gradient_norm)\n\nTERMINATING THE PROGRAM!\n', max_iter)
+    break; % Break out of while loop
+    
+elseif any(isnan(w2)) % If any of the weights become 'NaN' at any iteration
+    fprintf('Gradient Descent could not converge due to NaN values in w2 @ niter = %d \n\nTry to adjust the following parameters in the following order:\n1) rho\n2) max_iter\n3) tolerance ( < initial gradient_norm)\n\nTERMINATING THE PROGRAM!\n',niter)
+    break; % Break out of while loop
+end
+
+end % End of while loop
+
+% Printf number of iterations it took to converge (gradient descent)
+if niter < max_iter && ~any(isnan(w2))
+   fprintf('Number of iterations: %d\n', niter)
+end
+
+% Convert weights obtained from gradient descent with normalized data to
+% fit the un-normalized data (Not sure if necessary!)
+w2 = x\(xnorm*w2);
+y3 = x*w2;
+
+% Plot Gradient Descent solution line on the scatter plot of data
+figure(2)
+x = Data(:,1);
+y = Data(:,2);
+scatter(x,y,50,'x','r','LineWidth',2);
+title('Matlab''s "carbig" dataset');
+xlabel('Weight');
+ylabel('Horsepower');
+hold on;
+p5 = plot(x(:,1),y3, 'LineWidth',2, 'color', 'g');
+legend(p5,'Gradient Descent')
+hold off;
+
+% Plot & Monitor the Cost function (J) (OPTIONAL!)
+
+option = 'on'; % Choose 'on' or 'off' to turn on\off plot - CAN BE ADJUSTED! 
+
+if strcmp(option, 'on')
+figure(3)
+title('OPTIONAL PLOT: J(w) vs niter');
+xlabel('niter');
+ylabel('J(w)');
+hold on
+p2 = plot(1:niter,J, 'LineWidth',3, 'color', 'b');
+p3 = scatter(1,JJ,'x','g','LineWidth',10);
+p4 = scatter(niter,J(:,niter),'x','r','LineWidth',10);
+legend([p2, p3, p4],'Gradient Descent J(w)', 'Analytical solution optimum J(w)', 'Gradient Descent optimum J(w)')
+hold off
+elseif strcmp(option, 'off')
+    fprintf('J(w) vs niter is not plotted\nChange option to plot!\n');
+else
+    error('Please choose "on" or "off" to turn on/off plot. CHECK THE SPELLING!'); 
+end