偏最小二乘法matlab代码

以下是偏最小二乘法的MATLAB代码：

function [Xloadings,Yloadings,Xscores,Yscores,betaPLS,PLSPctVar] = plsregress(X,Y,ncomp)

% 偏最小二乘法回归函数
%
% 输入：
% X - nobs x nvar 矩阵，表示X矩阵
% Y - nobs x ny 矩阵，表示Y矩阵
% ncomp - scalar，表示所需成分数
%
% 输出：
% Xloadings - nvar x ncomp 矩阵，表示X矩阵的载荷
% Yloadings - ny x ncomp 矩阵，表示Y矩阵的载荷
% Xscores - nobs x ncomp 矩阵，表示X矩阵的得分
% Yscores - nobs x ncomp 矩阵，表示Y矩阵的得分
% betaPLS - nvar x ny x ncomp 矩阵，表示偏最小二乘法回归系数
% PLSPctVar - ncomp x 2 矩阵，表示每个成分的方差百分比

[nobs,nvar] = size(X);
ny = size(Y,2);

% 中心化X和Y
Xmean = mean(X);
Xstd = std(X);
X = (X - Xmean(ones(nobs,1),:))./Xstd(ones(nobs,1),:);

Ymean = mean(Y);
Ystd = std(Y);
Y = (Y - Ymean(ones(nobs,1),:))./Ystd(ones(nobs,1),:);

% 初始化载荷和得分矩阵
Xloadings = zeros(nvar,ncomp);
Yloadings = zeros(ny,ncomp);
Xscores = zeros(nobs,ncomp);
Yscores = zeros(nobs,ncomp);

% 初始化权重向量
w = X'*Y;
w = w./sqrt(sum(w.^2));

% 迭代计算成分
for i = 1:ncomp
% 计算X得分
t = X*w;
t = t./sqrt(sum(t.^2));
Xscores(:,i) = t;

% 计算Y得分
u = Y'*t;
u = u./sqrt(sum(u.^2));
Yscores(:,i) = Y*u;

% 计算X载荷
p = X'*t;
p = p./sqrt(sum(p.^2));
Xloadings(:,i) = p;

% 计算Y载荷
q = Y'*u;
q = q./sqrt(sum(q.^2));
Yloadings(:,i) = q;

% 计算回归系数
betaPLS(:,:,i) = inv(p'*p)*p'*Y*u';

% 计算残差矩阵
X = X - t*p';
Y = Y - t*betaPLS(:,:,i)'*q';

% 更新权重向量
w = X'*Y;
w = w./sqrt(sum(w.^2));
end

% 计算方差百分比
Xresiduals = X;
Yresiduals = Y;
totalVarX = sum(sum(Xresiduals.^2));
totalVarY = sum(sum(Yresiduals.^2));
for i = 1:ncomp
PLSPctVar(i,:) = [sum(sum(Xscores(:,1:i).^2))/totalVarX,...
sum(sum(Yscores(:,1:i).^2))/totalVarY];
end

% 反标准化载荷和得分
Xloadings = Xloadings./Xstd(:,ones(ncomp,1));
Yloadings = Yloadings./Ystd(:,ones(ncomp,1));
Xscores = Xscores*Xstd(:,ones(ncomp,1));
Yscores = Yscores*Ystd(:,ones(ncomp,1));

end