斯坦福大学-Logistic回归_Exercise Code

clear all; close all; clc

x = load('ex4x.dat');
y = load('ex4y.dat');

[m, n] = size(x);

% Add intercept term to x
x = [ones(m, 1), x];

% Plot the training data
% Use different markers for positives and negatives
figure
pos = find(y); neg = find(y == 0);%find是找到的一个向量，其结果是find函数括号值为真时的值的编号
plot(x(pos, 2), x(pos,3), '+')
hold on
plot(x(neg, 2), x(neg, 3), 'o')
hold on
xlabel('Exam 1 score')
ylabel('Exam 2 score')

% Initialize fitting parameters
theta = zeros(n+1, 1);

% Define the sigmoid function
g = inline('1.0 ./ (1.0 + exp(-z))');

% Newton's method
MAX_ITR = 7;
J = zeros(MAX_ITR, 1);

for i = 1:MAX_ITR
% Calculate the hypothesis function
z = x * theta;
h = g(z);%转换成logistic函数

% Calculate gradient and hessian.
% The formulas below are equivalent to the summation formulas
% given in the lecture videos.
grad = (1/m).*x' * (h-y);%梯度的矢量表示法
H = (1/m).*x' * diag(h) * diag(1-h) * x;%hessian矩阵的矢量表示法

% Calculate J (for testing convergence)
J(i) =(1/m)*sum(-y.*log(h) - (1-y).*log(1-h));%损失函数的矢量表示法

theta = theta - H\grad;
end
% Display theta
theta

% Calculate the probability that a student with
% Score 20 on exam 1 and score 80 on exam 2
% will not be admitted
prob = 1 - g([1, 20, 80]*theta)

%画出分界面
% Plot Newton's method result
% 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(plot_x, plot_y)
legend('Admitted', 'Not admitted', 'Decision Boundary')
hold off

% Plot J
figure
plot(0:MAX_ITR-1, J, 'o--', 'MarkerFaceColor', 'r', 'MarkerSize', 8)
xlabel('Iteration'); ylabel('J')
% Display J
J