%%Machine learning From Andrew with Matlab ex2
%%By youknowwho3_3 in 优快云 #GirlsHelpGirls#DOUBANEZU%%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 1and score 85 on exam 2
prob = sigmoid([14585]* 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 1lambda=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 withall-ones theta andlambda=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 isall-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
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