简单易学的机器学习算法——非线性支持向量机

%% 非线性支持向量机

% 清空内存
clear all;
clc;

% 导入测试数据
A = load('testSetRBF.txt');

%% 区分开训练数据与测试数据
m = size(A);%得到整个数据集的大小
trainA = A(11:m(1,1),:);
testA = A(1:10,:);

% 训练和测试数据集的大小
mTrain = size(trainA);
mTest = size(testA);

% 区分开特征与标签
Xtrain = trainA(:,1:2);
Ytrain = trainA(:,mTrain(1,2))';
Xtest = testA(:,1:2);
Ytest = testA(:,mTest(1,2))';

%% 对偶问题，用二次规划来求解，以求得训练模型
sigma = 0.5;%高斯核中的参数
H = zeros(mTrain(1,1),mTrain(1,1));
for i = 1:mTrain(1,1)
    for j = 1:mTrain(1,1)
        H(i,j) = GaussianKernalFunction(Xtrain(i,:),Xtrain(j,:),sigma);
        H(i,j) = H(i,j)*Ytrain(i)*Ytrain(j);
    end
end

f = ones(mTrain(1,1),1)*(-1);
B = Ytrain;
b = 0;
lb = zeros(mTrain(1,1),1);
% 调用二次规划的函数
[x,fval,exitflag,output,lambda] = quadprog(H,f,[],[],B,b,lb);

% 定义C
C = max(x);

% 求解原问题
n = size(x);
k = 1;
for i = 1:n(1,1)
    Kernel = zeros(n(1,1),1);
    if x(i,1) > 0 && x(i,1)<C
        for j = 1:n(1,1)
            Kernel(j,:) = GaussianKernalFunction(Xtrain(j,:),Xtrain(i,:),sigma);
            Kernel(j,:) = Kernel(j,:)*Ytrain(j);
        end
        b(k,1) = Ytrain(1,i)-x'*Kernel;
        k = k +1;
    end
end
b = mean(b);


%% 决策函数来验证训练准确性
trainOutput = zeros(mTrain(1,1),1);
for i = 1:mTrain(1,1)
    Kernel_train = zeros(mTrain(1,1),1);
    
    for j = 1:mTrain(1,1)
        Kernel_train(j,:) = GaussianKernalFunction(Xtrain(j,:),Xtrain(i,:),sigma);
        Kernel_train(j,:) = Kernel_train(j,:)*Ytrain(j);
    end
    trainOutput(i,1) = x'*Kernel_train+b;
end

for i = 1:mTrain(1,1)
    if trainOutput(i,1)>0
        trainOutput(i,1)=1;
    elseif trainOutput(i,1)<0
        trainOutput(i,1)=-1;
    end
end

% 统计正确个数
countTrain = 0;
for i = 1:mTrain(1,1)
    if trainOutput(i,1) == Ytrain(i)
        countTrain = countTrain+1;
    end
end
trainCorrect = countTrain./mTrain(1,1);

%% 决策函数来验证测试准确性
testOutput = zeros(mTest(1,1),1);
for i = 1:mTest(1,1)
    Kernel_test = zeros(mTrain(1,1),1);
    
    for j = 1:mTrain(1,1)
        Kernel_test(j,:) = GaussianKernalFunction(Xtrain(j,:),Xtest(i,:),sigma);
        Kernel_test(j,:) = Kernel_test(j,:)*Ytrain(j);
    end
    testOutput(i,1) = x'*Kernel_train+b;
end

for i = 1:mTest(1,1)
    if testOutput(i,1)>0
        testOutput(i,1)=1;
    elseif testOutput(i,1)<0
        testOutput(i,1)=-1;
    end
end

% 统计正确个数
countTest = 0;
for i = 1:mTest(1,1)
    if testOutput(i,1) == Ytest(i)
        countTest = countTest+1;
    end
end
testCorrect = countTest./mTest(1,1);

disp(['训练的准确性：',num2str(trainCorrect)]);
disp(['测试的准确性：',num2str(testCorrect)]);

%% 高斯核函数，其中输入x和y都是行向量
function [ output ] = GaussianKernalFunction( x,y,sigma )
    output = exp(-(x-y)*(x-y)'./(2*sigma^2));
end