3.3编程实现对率回归，并给出西瓜数据集3.0α上的结果

数据集：

• 1 0.697 0.460 1
  2 0.774 0.376 1
  3 0.634 0.264 1
  4 0.608 0.318 1
  5 0.556 0.215 1
  6 0.403 0.237 1
  7 0.481 0.149 1
  8 0.437 0.211 1
  9 0.666 0.091 0
  10 0.243 0.267 0
  11 0.245 0.057 0
  12 0.343 0.099 0
  13 0.639 0.161 0
  14 0.657 0.198 0
  15 0.360 0.370 0
  16 0.593 0.042 0
  17 0.719 0.103 0

MATLAB 代码

clear
clc
data = load('gua.txt');  
X = data(:, [2, 3]); y = data(:, 4);  
figure; 
hold on;  
pos=find(y==1);  
neg=find(y==0); 
data(pos,4)
plot(X(pos,1),X(pos,2),'g.','LineWidth',2,'MarkerSize',7);  
plot(X(neg,1),X(neg,2),'k.','MarkerFaceColor','y','MarkerSize',7);  
% Labels and Legend  
xlabel('密度')  
ylabel('含糖率')  
hold off;  
[m, n] = size(X) ;
% Add intercept term to x and X_test  
X = [X ones(m, 1) ];
% Initialize fitting parameters  
initial_theta = zeros(n + 1, 1)  ;
options = optimset('GradObj', 'on', 'MaxIter', 400);  
[theta, cost] = fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);  
hold on;
    plot_x = X(:,1) ; 
    y = X*theta ;
    plot_y=1./(1.+exp(-1.*y))
    plot(plot_x, plot_y,'r+','LineWidth',2,'MarkerSize',7)    
hold off;  

function [J, grad] = costFunction(theta, X, y)  
m = length(y); % number of training examples  
J = 0;  
grad = zeros(size(theta));  
h=1.0./(1.0+exp(-1*X*theta));  
m=size(y,1);  
J=((-1*y)'*log(h)-(1-y)'*log(1-h))/m;  
for i=1:size(theta,1),  
    grad(i)=((h-y)'*X(:,i))/m;  
end  
end  

结果：

黑点负例
绿点正例
红点 X轴密度，y轴y值
结果：

• 0.971079254646882 1
  0.937598463307093 1
  0.705751586241412 1
  0.812393063785119 1
  0.504856248448885 1
  0.453265086556073 0
  0.261482588297326 0
  0.400249657018173 0
  0.235208808199154 0
  0.421463325239397 0
  0.0508913086555173 0
  0.109609784911483 0
  0.403185071514151 0
  0.531250393637467 1
  0.791459430045055 1
  0.117240356541242 0
  0.296693337407861 0

以0.5做阈值：数据太少，不太好