PLS.rar_PLS偏最小二乘法_偏最小二乘

function [T,P,U,Q,B,W] = pls (X,Y,tol2) % PLS Partial Least Squares Regrassion % % [T,P,U,Q,B,Q] = pls(X,Y,tol) performs particial least squares regrassion % between the independent variables, X and dependent Y as % X = T*P' + E; % Y = U*Q' + F = T*B*Q' + F1; % % Inputs: % X data matrix of independent variables % Y data matrix of dependent variables % tol the tolerant of convergence (defaut 1e-10) % % Outputs: % T score matrix of X % P loading matrix of X % U score matrix of Y % Q loading matrix of Y % B matrix of regression coefficient % W weight matrix of X % % Using the PLS model, for new X1, Y1 can be predicted as % Y1 = (X1*P)*B*Q' = X1*(P*B*Q') % or % Y1 = X1*(W*inv(P'*W)*inv(T'*T)*T'*Y) % % Without Y provided, the function will return the principal components as % X = T*P' + E % % Example: taken from Geladi, P. and Kowalski, B.R., "An example of 2-block % predictive partial least-squares regression with simulated data", % Analytica Chemica Acta, 185(1996) 19--32. %{ x=[4 9 6 7 7 8 3 2;6 15 10 15 17 22 9 4;8 21 14 23 27 36 15 6; 10 21 14 13 11 10 3 4; 12 27 18 21 21 24 9 6; 14 33 22 29 31 38 15 8; 16 33 22 19 15 12 3 6; 18 39 26 27 25 26 9 8;20 45 30 35 35 40 15 10]; y=[1 1;3 1;5 1;1 3;3 3;5 3;1 5;3 5;5 5]; % leave the last sample for test N=size(x,1); x1=x(1:N-1,:); y1=y(1:N-1,:); x2=x(N,:); y2=y(N,:); % normalization xmean=mean(x1); xstd=std(x1); ymean=mean(y1); ystd=std(y); X=(x1-xmean(ones(N-1,1),:))./xstd(ones(N-1,1),:); Y=(y1-ymean(ones(N-1,1),:))./ystd(ones(N-1,1),:); % PLS model [T,P,U,Q,B,W]=pls(X,Y); % Prediction and error yp = (x2-xmean)./xstd * (P*B*Q'); fprintf('Prediction error: %g\n',norm(yp-(y2-ymean)./ystd)); %} % % By Yi Cao at Cranfield University on 2nd Febuary 2008 % % Reference: % Geladi, P and Kowalski, B.R., "Partial Least-Squares Regression: A % Tutorial", Analytica Chimica Acta, 185 (1986) 1--7. % % Input check error(nargchk(1,3,nargin)); error(nargoutchk(0,6,nargout)); if nargin<2 Y=X; end tol = 1e-10; if nargin<3 tol2=1e-10; end % Size of x and y [rX,cX] = size(X); [rY,cY] = size(Y); assert(rX==rY,'Sizes of X and Y mismatch.'); % Allocate memory to the maximum size n=max(cX,cY); T=zeros(rX,n); P=zeros(cX,n); U=zeros(rY,n); Q=zeros(cY,n); %特征向量按X,Y中的独立变量较多的个数来设置，这里为4，X,Y的投影向量是成对出现的，即使，Y的最后一个特征向量可由前三个线性表示 B=zeros(n,n); W=P; k=0; % iteration loop if residual is larger than specfied while norm(Y)>tol2 && k<n %tol2 控制残差的范围限度 % choose the column of x has the largest square of sum as t. % choose the column of y has the largest square of sum as u. [dummy,tidx] = max(sum(X.*X)); [dummy,uidx] = max(sum(Y.*Y)); t1 = X(:,tidx); u = Y(:,uidx); t = zeros(rX,1); % iteration for outer modeling until convergence while norm(t1-t) > tol w = X'*u; w = w/norm(w); t = t1; t1 = X*w; q = Y'*t1; q = q/norm(q); u = Y*q; end % update p based on t t=t1; p=X'*t/(t'*t); pnorm=norm(p);%C:\Program Files\MATLAB\R2016a\toolbox\mpc\mpcobsolete\plsr.m % p=p/pnorm; %t=t*pnorm; % w=w*pnorm; % regression and residuals b = u'*t/(t'*t); X = X - t*p'; Y = Y - b*t*q'; %这里的b*t=u % save iteration results to outputs: k=k+1; T(:,k)=t; P(:,k)=p; U(:,k)=u; Q(:,k)=q; W(:,k)=w; B(k,k)=b; % uncomment the following line if you wish to see the convergence % disp(norm(Y)) end T(:,k+1:end)=[]; P(:,k+1:end)=[]; U(:,k+1:end)=[]; Q(:,k+1:end)=[]; W(:,k+1:end)=[]; B=B(1:k,1:k);