转行程序员4 机器学习 Regularization 纯属敦促自己学习

作业 网址 http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=MachineLearning&doc=exercises/ex5/ex5.html
所编写的代码

% Exercise 5 -- Linear Regression

close all;clear;clc;

x = load('ex5Linx.dat');

y = load('ex5Liny.dat');

figure;

plot(x,y,'o','MarkerFaceColor', 'r', 'MarkerSize', 8);

m = length(y);

x = [ones(m, 1), x, x.^2, x.^3, x.^4, x.^5];

lamda = 1; % 惩罚系数

matrix = diag([0,ones(1,5)] );

theta = (x'*x+lamda.*matrix)\x'*y;

hold on

plot_x = [min(x(:,2)):0.05:max(x(:,2))+0.2]';

plot_y = [ones(length(plot_x), 1), plot_x, plot_x.^2, plot_x.^3, plot_x.^4, plot_x.^5]*theta;

plot(plot_x,plot_y,'--');

legend('Training data','5thorder fit ')

% Exercise 5 -- Logistic Regression using Newton's method

close all;clear;clc;

x = load('ex5Logx.dat');

y = load('ex5Logy.dat');

figure;

% Find the indices for the 2 classes

pos = find(y); neg = find(y == 0);

plot(x(pos, 1), x(pos, 2), '+')

hold on

plot(x(neg, 1), x(neg, 2), 'o','MarkerFaceColor', 'y', 'MarkerSize', 8)

legend('y=1','y=0');

u = x(:,1);

v = x(:,2);

x = map_feature(u, v);

m=length(y);

g = inline('1.0 ./ (1.0 + exp(-z))');

theta = zeros(28,1);

MAX_ITR = 15;

lamda = 1;

matrix = diag([0,ones(1,27)] );

J = zeros(MAX_ITR, 1);

for i=1:MAX_ITR

    

    zz = x * theta;

    h = g(zz);

    grad = (1/m).*x' * (h-y)+lamda/m.*matrix*theta;

    H = (1/m).*x' * diag(h) * diag(1-h) * x+(lamda/m).*matrix;

    theta = theta - H\grad;

    J(i) =(1/m)*sum(-y.*log(h) - (1-y).*log(1-h));

end

% Define the ranges of the grid

u = linspace(-1, 1.5, 200);

v = linspace(-1, 1.5, 200);

% Initialize space for the values to be plotted

z = zeros(length(u), length(v));

% Evaluate z = theta*x over the grid

for i = 1:length(u)

    for j = 1:length(v)

        % Notice the order of j, i here!

        z(j,i) = map_feature(u(i), v(j))*theta;

    end

end

contour(u,v,z, [0, 0], 'LineWidth', 2)

% Plot J

figure

plot(0:MAX_ITR-1, J, 'o--', 'MarkerFaceColor', 'r', 'MarkerSize', 8)

xlabel('Iteration'); ylabel('J')