%%Machine learning From Andrew with Matlab ex2
%%By youknowwho3_3 in CSDN
%%logistic regression's
%1.sigmoid function
%2.compute costFunction for logistic regression
%3.Gradient for logistic regression
%4.predict function
%5.compute cost for regularized LR
%6.Gradient for regularized Logistic regression
%%
%%%%%%%%%%%%logistic regression%%%%%%%%%%%
%%ploat data
data=load("ex2data1.txt");
x = data(:, [1, 2]);
y = data(:, 3);
%%%%%x1,x2两门课的成绩，y出席与否
% Plot the data with + indicating (y = 1) examples and o indicating (y = 0) examples.
plotData(x, y);
% Labels and Legend
xlabel('Exam 1 score')
ylabel('Exam 2 score')
% Specified in plot order
legend(' ', 'Not admitted')
%%implementation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%costFunciton&Gradient Descent for Logistc Regression%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Setup the data matrix appropriately
[m, n] = size(x);
% Add intercept term to X
X = [ones(m, 1) x];
% Initialize the fitting parameters
initial_theta = zeros(n + 1, 1);
[cost,grad]=costFunction(initial_theta,X,y);
fprintf('TheValueOfCost: %f\n',cost)
disp('Gradient at initial theta (zeros):');
disp(grad);
%TheValueOfCost: 0.693147
%Gradient at initial theta (zeros):
% -0.1000
% -12.0092
% -11.2628
%%call 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);
disp('theta:');disp(theta);
% Plot Boundary
plotDecisionBoundary(theta, X, y);
% Add some labels
hold on;
% Labels and Legend
xlabel('Exam 1 score')
ylabel('Exam 2 score')
% Specified in plot order
legend('Admitted', 'Not admitted')
hold off;
% Predict probability of admition for a student with score 45 on exam 1 and score 85 on exam 2
prob = sigmoid([1 45 85] * theta);%%New h
fprintf('For a student with scores 45 and 85, we predict an admission probability of %f\n\n', prob);
% Compute accuracy on our training set
p = predict(theta, X);
fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
%%%%%%%%Regularized logistic regression%%%%%%%%%
% The first two columns contains the X values and the third column
% contains the label (y).
data = load('ex2data2.txt');
X = data(:, [1, 2]); y = data(:, 3);
plotData(X, y);
% Put some labels
hold on;
% Labels and Legend
xlabel('Microchip Test 1')
ylabel('Microchip Test 2')
% Specified in plot order
legend('y = 1', 'y = 0')
hold off;
% Add Polynomial Features
% Note that mapFeature also adds a column of ones for us, so the intercept term is handled
X = mapFeature(X(:,1), X(:,2));
%%calling costFunctionReg
% Initialize fitting parameters
initial_theta = zeros(size(X, 2), 1);
% Set regularization parameter lambda to 1
lambda = 1;
% Compute and display initial cost and gradient for regularized logistic regression
[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
fprintf('Cost at initial theta (zeros): %f\n', cost);
fprintf('Expected cost (approx): 0.693\n');
fprintf('Gradient at initial theta (zeros) - first five values only:\n');
fprintf(' %f \n', grad(1:5));
fprintf('Expected gradients (approx) - first five values only:\n');
fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');
% Compute and display cost and gradient with all-ones theta and lambda = 10
test_theta = ones(size(X,2),1);
[cost, grad] = costFunctionReg(test_theta, X, y, 10);
fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
fprintf('Expected cost (approx): 3.16\n');
fprintf('Gradient at test theta - first five values only:\n');
fprintf(' %f \n', grad(1:5));
fprintf('Expected gradients (approx) - first five values only:\n');
fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');
%%function costFunctionReg
%{
formulate:%costFunction
J=1/m*sum(i=1:m)[-yi*log(h(xi))-(1-yi)*log(1-h(xi))]+lambda/2m*sum(j=1:n)(theta^2)
%gradientDescent
theta(j)
j=0 J'=1/m*sum(h(xi)-yi)*xi
j>=1 J'=1/m*sum(h(xi)-yi)*xi+lambda/m*theta(j)
code: h=sigmoid(z)
z=X*theta
J=1/m*sum(-y.*log(h)-(1-y).*log(1-h))+lambda/(2*m)*sum(theta(2:end).^2)
j=0 grad(1) = (1/m)* (X(:,1)'*(h-y));
j>=1 grad(2:end) = (1/m)* (X(:,2:end)'*(h-y))+(lambda/m)*theta(2:end);
%}
function [J, grad] = costFunctionReg(theta, X, y, lambda)
m=length(y);
J = 0;
grad = zeros(size(theta));
z = X * theta; % m x 1
h = sigmoid(z); % m x 1
J=1/m*sum(-y.*log(h)-(1-y).*log(1-h))+lambda/(2*m)*sum(theta(2:end).^2);
grad(1) = (1/m)* (X(:,1)'*(h-y)); % 1 x 1
grad(2:end) = (1/m)* (X(:,2:end)'*(h-y))+(lambda/m)*theta(2:end); % n x 1
end
%%function mapFeature
function out = mapFeature(X1, X2)
% MAPFEATURE Feature mapping function to polynomial features
% MAPFEATURE(X1, X2) maps the two input features
% to quadratic features used in the regularization exercise.
%
% Returns a new feature array with more features, comprising of
% X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..
%
% Inputs X1, X2 must be the same size
degree = 6;
out = ones(size(X1(:,1)));
for i = 1:degree
for j = 0:i
out(:, end+1) = (X1.^(i-j)).*(X2.^j);
end
end
end
%%Predict Function
function p=predict(theta,X)
m = size(X, 1);
p = zeros(m, 1);
h= sigmoid(X*theta);
p=(h>=0.5);
end
%%plotDecisionBoundary Function (prepared)
function plotDecisionBoundary(theta, X, y)
%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
%the decision boundary defined by theta
% PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the
% positive examples and o for the negative examples. X is assumed to be
% a either
% 1) Mx3 matrix, where the first column is an all-ones column for the
% intercept.
% 2) MxN, N>3 matrix, where the first column is all-ones
plotData(X(:,2:3), y);
hold on
if size(X, 2) <= 3
% Only need 2 points to define a line, so choose two endpoints
plot_x = [min(X(:,2))-2, max(X(:,2))+2];
% Calculate the decision boundary line
plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
% Plot, and adjust axes for better viewing
plot(plot_x, plot_y)
% Legend, specific for the exercise
legend('Admitted', 'Not admitted', 'Decision Boundary')
axis([30, 100, 30, 100])
else
% Here is the grid range
u = linspace(-1, 1.5, 50);
v = linspace(-1, 1.5, 50);
z = zeros(length(u), length(v));
% Evaluate z = theta*x over the grid
for i = 1:length(u)
for j = 1:length(v)
z(i,j) = mapFeature(u(i), v(j))*theta;
end
end
z = z'; % important to transpose z before calling contour
% Plot z = 0
% Notice you need to specify the range [0, 0]
contour(u, v, z, [0, 0], 'LineWidth', 2)
end
hold off
end
%%plotData Function
function plotData(X,y)
% Find Indices of Positive and Negative Examples
pos = find(y==1); %Everytime find y==1, pos targets the X.
neg = find(y==0);
% Plot Examples
plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2, 'MarkerSize', 7);
hold on;%%%%%%%%%%%%%%%%%%%%%Attention:The original Code do not hold it.But you should add it.
plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y','MarkerSize', 7);
hold off;%%%%%%%%%%%%%%%%%%%%%Attention:The original Code do not hold it.But you should add it.
%%%%%%hold on & off is helpful to plot two data.
end
%costFunction of logistic regression
%formulate J(theta)=1/m*sum[-yi*log(h(xi)-(1-yi)*log(1-h(xi))]
% J在theta的导数=grad=1/m*sum((hxi-yi)xi)
% h(X)=g(theta'*X)
% g(z)=1/(1+e^(-z))
%for coding h=sigmoid(X*theta) size(X*theta)=100*1
% sigmoid(z)=1./(1+exp(-z))
% size(1./(1+exp(-X*theta))=size(h)=100*1
% Not size(1/(1+exp(-X*theta))=1*100
% J=1/m*sum(-y.*log(h)-(1-y).*log(1-h))
% size(log(h))=100*1
% size(y)=100*1 so elements in y multiple log(h)
% if size(y'*log(h))=1*1 its not we want.
%%%%% grad=1/m*X'*(h-y) size(X')=3*100 size(h-y)=100*1
%%%%% size(grad)=3*1
function [J,Grad]=costFunction(theta,X,y)
m=length(y);
Grad=zeros(size(theta));
h=sigmoid(X*theta);
J=1/m*sum(-y.*log(h)-(1-y).*log(1-h));
Grad=1/m*X'*(h-y);
end
%%sigmoid function
%Formula:h(X)=g(theta'*X)=1/(1+e^(-theta'*X))
% Coding:h=1./(1+exp(-X*theta))
function g=sigmoid(z)
g=zeros(size(z));
g=1./(1+exp(-z));
end
