机器学习 logstic 实现二分类（matlab）

实现：

figure;
pos = find(label == 1); neg = find(label == 0);
plot(data(pos, 1), data(pos,2), '+')
hold on
plot(data(neg, 1), data(neg, 2), 'o')
hold on
xlabel('Exam 1 score')
ylabel('Exam 2 score')
%调用函数 求代价和迭代值
[theta J] = logsticTest(data,label);
plot_x = [min(data(:,1))-2,  max(data(:,1))+2];
plot_y = (-1./theta(3)).*(theta(2).*plot_x +theta(1)); %theta(1) + theta(2)x + theta(3)y = 0 转化为直线
plot(plot_x,plot_y,'g');
hold off;
MAX_ITR = 7;
figure;
plot(0:MAX_ITR-1, J, 'o--', 'MarkerFaceColor', 'r', 'MarkerSize', 8)
xlabel('Iteration'); ylabel('J');

logsticTest函数：

function [theta J] = logsticTest(x,y)

[m,n] = size(x);
x = [ones(m,1),x];%添加第一列全为1
theta = zeros(n+1, 1);

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

% Newton's method
MAX_ITR = 7;%最大迭代次数
J = zeros(MAX_ITR, 1);

for i = 1:MAX_ITR
    % Calculate the hypothesis function
    z = x * theta;%列向量
    h = g(z);%计算sigmoid值 为列向量
    % Calculate gradient and hessian.
    % The formulas below are equivalent to the summation formulas
    % given in the lecture videos.
    grad = (1/m).*x' * (h-y);% 得到列向量 表示 theta(0),theta(1) ... theta(i),的偏导得到的
    H = (1/m).* (x'*diag(h) * diag(1-h)*x);%这里采用 对角阵的方式实现 分别的对第i行数据乘积
    % Calculate J (for testing convergence)
    J(i) =(1/m)*sum(-y.*log(h) - (1-y).*log(1-h));
    theta = theta - H\grad;
end

分类结果：

迭代过程：

数据下面的连接中有

参考：点击打开链接

参考：点击打开链接