lssvm.m

可以利用最小二乘支持向量机进行训练和预测

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%最小二乘支持向量机（LSSVM）软测量，崔宇，200901
%该函数的作用：用训练样本集进行训练，然后对测试样本集进行预测，返回预测输出值
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%【输入】： XTrain   - 训练集样本_锅炉工况数据
%          yTrain   - 训练集样本_飞灰含碳(或烟气含氧)真实值
%          XTest    - 测试集样本_锅炉工况
%          Gama     - 惩罚系数（LS-SVM参数，也叫正规化参数）
%          Sigma    - RBF核函数参数（LS-SVM参数）
%【输出】：yPredict - 飞灰含碳(或烟气含氧)软测量模型预测值

function yPredict= LSSVM(XTrain,yTrain,XTest,Gama,Sigma);

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%初始化
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% t = cputime;
SampleNumber = size(XTrain,1);   %训练样本数（各论文中的“L”）

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%LSSVM方法中，线性方程组等号左边的系数矩阵
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InputMatrix =ones(SampleNumber + 1,SampleNumber + 1);  %初始化线性方程组等号左边的矩阵
InputMatrix(1,1) =0;
KernelXTrain = zeros(SampleNumber,SampleNumber);  %初始化线性方程组等号左边的矩阵中的子阵
%对线性方程等号左边的矩阵中的子阵进行赋值
for i = 1:SampleNumber
    
    for j = 1:SampleNumber
        
        if i < j,                   
            KernelXTrain(i,j) = sum((XTrain(j,:) - XTrain(i,:)).^2); %欧式距离的平方
        else
            KernelXTrain(i,j) = KernelXTrain(j,i);
        end
        
    end

end
%计算线性方程组等号左边矩阵
KernelXTrain = exp(KernelXTrain/-Sigma);
KernelXTrain =KernelXTrain + 1 / Gama * eye(SampleNumber);
InputMatrix(2:SampleNumber + 1,2:SampleNumber + 1) = KernelXTrain;

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%LSSVM方法中，线性方程组等号右边的系数矩阵
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OutMatrix = zeros(SampleNumber + 1,size(yTrain,2)); %初始化线性方程组等号右边的矩阵
%计算线性方程组右边矩阵
for i = 1:size(yTrain,2)
    OutMatrix(:,i) = [0;yTrain(:,i)];
end    
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%%求解LSSVM中的线性方程组
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Coefficient = inv(InputMatrix) * OutMatrix;
a = Coefficient(2:SampleNumber + 1,:);
b=zeros(size(XTest,1),1);
for i = 1:size(XTest,1)
    b(i,:) = Coefficient(1,:);
end

% cputime - t
% t1= cputime;

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%%计算测试集锅炉工况核函数
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KernelXTest= zeros(size(XTest,1),SampleNumber);
for i = 1:size(XTest,1)
    
    for j = 1:SampleNumber
        KernelXTest(i,j) = sum((XTrain(j,:) - XTest(i,:)).^2);  %欧式距离的平方
    end
    
end
KernelXTest = exp(KernelXTest / -Sigma);

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%使用训练得到的软测量模型，对某一个（或几个）工况下的飞灰含碳（或烟气含氧）进行预测
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yPredict = KernelXTest * a + b;

% (cputime - t1)/SampleNumber

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%存在的若干问题
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