機器學習基石(Machine Learning Foundations) 机器学习基石作业四 Q13-20 MATLAB实现

大家好，我是Mac Jiang,今天和大家分享Coursera-NTU-機器學習基石（Machine Learning Foundations）-作业四 Q13-20的MATLAB实现。

曾经的代码都是通过C++实现的。可是发现C++实现这些代码太麻烦。这次作业还要频繁更改參数值，所以选择用MATLAB实现了。与C++相比。MATLAB实现显然轻松非常多。在数据导入方面也更加方便。我的代码尽管可以得到正确答案，可是当中可能有某些思想或者细节是错误的，假设各位博友发现，请及时留言纠正，谢谢。再次声明，博主提供实现代码的原因不是为了让各位通过測试，而是为学习有困难的同学提供一条解决思路。希望我的文章对您的学习有一些帮助！

本文出处：http://blog.csdn.net/a1015553840/article/details/51173020

其它问题解答请看汇总帖：http://blog.csdn.net/a1015553840/article/details/51085129

1.sign函数

function S = sign(x)  %计算sign
[m,n] = size(x);
for i = 1:m,
    for j = 1:n;

        if x(i,j) <= 0,
            S = 1;
        else
            S = -1;
        end
    end
end
end

2.计算正则化线性回归函数LGwithRegularization

function Wreg = LGwithRegularization(X,y,lambda)
[m,n] = size(X);
Wreg = inv(X' * X + lambda * eye(n)) * X' * y;%正则化的线性回归求解
end

3.错误计算函数Error01 (注意。这里用的是0/1错误)

function E = Error01(X,y,Wreg)
[m,n] = size(X);
E = 1 - sum(sign(X * Wreg) == y) / m;%计算错误率
end

4.主进程

clc
trainingData = load('trainingData.txt');
Xtrain = trainingData(:, [1, 2]); ytrain = trainingData(:, 3);
testData = load('testData.txt');
Xtest = testData(:,[1,2]);ytest = testData(:,3);
[m,n] = size(Xtrain);
Xtrain = [ones(m,1), Xtrain];
[a,b] = size(Xtest);
Xtest = [ones(a,1), Xtest];

%13-15
%lambda = 10^-3;
%Wreg = LGwithRegularization(Xtrain,ytrain,lambda);
%Ein = Error01(Xtrain,ytrain,Wreg)
%Eout = Error01(Xtest,ytest,Wreg)

%16-17
%lambda = 10^-3;
%Wreg = LGwithRegularization(Xtrain(1:120,:),ytrain(1:120,:),lambda);
%Etrain = Error01(Xtrain(1:120,:),ytrain(1:120,:),Wreg)
%Eval = Error01(Xtrain(121:200,:),ytrain(121:200,:),Wreg)
%Eout = Error01(Xtest,ytest,Wreg)

%18
%lambda = 10^0;
%Wreg = LGwithRegularization(Xtrain,ytrain,lambda);
%Ein = Error01(Xtrain,ytrain,Wreg)
%Eout = Error01(Xtest,ytest,Wreg)

%19
%lambda = 10^-6
%Ecv = 0;
%v = 5;
%per = m / v;
%for i = 1:v,
%    Xtemp = Xtrain;
%    ytemp = ytrain;
%    Xtemp(1+(i-1)*per:i*per,:) = [];%出去用于求交叉验证的样本
%    ytemp(1+(i-1)*per:i*per,:) = [];
%    Wreg = LGwithRegularization(Xtemp,ytemp,lambda);
%    Error01(Xtrain(1+(i-1)*per:i*per,:),ytrain(1+(i-1)*per:i*per,:),Wreg)%利用交叉验证的样本求Ecv
%    Ecv = Ecv + Error01(Xtrain(1+(i-1)*per:i*per,:),ytrain(1+(i-1)*per:i*per,:),Wreg);
%end
%Ecv = Ecv / v

%20
%lambda = 10^-8;
%Wreg = LGwithRegularization(Xtrain,ytrain,lambda);
%Ein = Error01(Xtrain,ytrain,Wreg)
%Eout = Error01(Xtest,ytest,Wreg)

13.第十三题

（1）题意：从两个站点下载训练样本和測试样本，利用正则化的线性回归，參数lambda取10。得到Ein 和Eout