machine-learning-ex2_1

%% Load Data

data = load('ex2data1.txt');
X = data(:, [1, 2]); y = data(:, 3);

%%Plotting

plotData(X, y);

function plotData(X, y)figure;hold on;pos=find(y==1);neg=find(y==0);plot(X(pos,1),X(pos,2),'k+','LineWidth',2,...    'MarkerSize',7);plot(X(neg,1),X(neg,2),'ko','MarkerFaceColor','y',...    'MarkerSize',7);hold off;end

hold on;

xlabel('Exam 1 score')
ylabel('Exam 2 score')

legend('Admitted', 'Not admitted')
hold off;

%%Compute Cost and Gradient

[m, n] = size(X);

X = [ones(m, 1) X];

initial_theta = zeros(n + 1, 1);

[cost, grad] = costFunction(initial_theta, X, y);

function [J, grad] = costFunction(theta, X, y)m = length(y);J = 0;grad = zeros(size(theta));sig=sigmoid(X * theta);J=-(1/m)*sum(y' * log(sig)+ (1-y') * log(1- sig));grad=(1/m )* (X'* (sig-y));end

fprintf('Cost at initial theta (zeros): %f\n', cost);
fprintf('Gradient at initial theta (zeros): \n');
fprintf(' %f \n', grad);
%%Optimizing using fminunc

options = optimset('GradObj', 'on', 'MaxIter', 400);

[theta, cost] = ...
fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);

fprintf('Cost at theta found by fminunc: %f\n', cost);

fprintf('theta: \n');
fprintf(' %f \n', theta);

plotDecisionBoundary(theta, X, y);

function plotDecisionBoundary(theta, X, y)plotData(X(:,2:3), y);hold onif size(X, 2) <= 3    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));    plot(plot_x, plot_y)    legend('Admitted', 'Not admitted', 'Decision Boundary')    axis([30, 100, 30, 100])else    u = linspace(-1, 1.5, 50);    v = linspace(-1, 1.5, 50);    z = zeros(length(u), length(v));    for i = 1:length(u)        for j = 1:length(v)            z(i,j) = mapFeature(u(i), v(j))*theta;        end    end    z = z';   contour(u, v, z, [0, 0], 'LineWidth', 2)endhold offend

hold on;

xlabel('Exam 1 score')

ylabel('Exam 2 score')
legend('Admitted', 'Not admitted')
hold off;

 %%Predict and Accuracies

prob = sigmoid([1 45 85] * theta);

function g = sigmoid(z)g = zeros(size(z));g=1./(1+exp(-z));end

fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
         'probability of %f\n\n'], prob);

p = predict(theta, X);

function p = predict(theta, X)m = size(X, 1);p = zeros(m, 1);sig=sigmoid(X * theta);for iter=1:m    if sig(iter)>=0.5        p(iter)=1;    else         p(iter)=0;    end;end;end

fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
fprintf('\nProgram paused. Press enter to continue.\n');
pause;