偏最小二乘法PLS回归NIPALS算法的Matlab程序及例子

本文格式为Word版，下载可任意编辑——偏最小二乘法PLS回归NIPALS算法的Matlab程序及例子偏最小二乘法PLS回归NIPALS算法的Matlab程序及例子②

function[T,P,W,Wstar,U,b,C,B_pls,...

Bpls_star,Xori_rec,Yori_rec,...

R2_X,R2_Y]=PLS_nipals(X,Y,nfactor)

%USAGE:[T,P,W,Wstar,U,b,C,Bpls,Bpls_star,Xhat,Yhat,R2X,R2Y]=PLS_nipals(X,Y,nfact)%PLSregressionNIPALSalgorithmPLS回归NIPALS算法

%ComputethePLSregressioncoefficientsPLS回归系数的计算%X=T*P'Y=T*B*C'=X*BplsXandYbeingZ-scores%B=diag(b)

%Y=X*Bpls_starwithXbeingaugmentedwithacolofones%andYandXhavingtheiroriginalunits%T'*T=I(NBnormalizationSAS)%W'*W=I%

%TestforPLSregression

%HerveAbdiNovember2002/revNovember2004%%

%VersionwithT,W,andCbeingunitnormalized%U,Parenot

%nfact=numberoflatentvariablestokeep保持潜在变量的数量%default=rank(X)

X_ori=X;Y_ori=Y;

ifexist('nfactor')~=1;nfactor=rank(X);endM_X=mean(X);M_Y=mean(Y);S_X=std(X);S_Y=std(Y);X=zscore(X);Y=zscore(Y);[nn,np]=size(X);[n,nq]=size(Y);ifnn~=n;

error(['Incompatible#ofrowsforXandY']);end

%Precisionforconvergenceepsilon=eps;

%#ofcomponentskepts%Initialistion%TheYset

U=zeros(n,nfactor);

C=zeros(nq,nfactor);%TheXset

T=zeros(n,nfactor);P=zeros(np,nfactor);W=zeros(np,nfactor);b=zeros(1,nfactor);R2_X=zeros(1,nfactor);R2_Y=zeros(1,nfactor);Xres=X;Yres=Y;

SS_X=sum(sum(X.^2));SS_Y=sum(sum(Y.^2));forl=1:nfactor

t=normaliz(Yres(:,1));

t0=normaliz(rand(n,1)*10);u=t;

nstep=0;

maxstep=100;

while(((t0-t)'*(t0-t)>epsilon/2)nstep=nstep+1;

disp(['LatentVariable#',int2str(l),'Iteration#:',int2str(nstep)])t0=t;

w=normaliz(Xres'*u);t=normaliz(Xres*w);%t=Xres*w;

c=normaliz(Yres'*t);

u=Yres*c;end;

disp(['LatentVariable#',int2str(l),',convergencereachedatstep',...int2str(nstep)]);%Xloadingsp=Xres'*t;%bcoef

b_l=((t'*t)^(-1))*(u'*t);b_1=u'*t;

%Storeinmatricesb(l)=b_l;P(:,l)=p;W(:,l)=w;T(:,l)=t;U(:,l)=u;C(:,l)=c;

%deflationofXandYXres=Xres-t*p';

Yres=Yres-(b(l)*(t*c'));

R2_X(l)=(t'*t)*(p'*p)./SS_X;

R2_Y(l)=(t'*t)*(b(l).^2)*(c'*c)./SS_Y;end

%Yhat=X*B_pls;X_rec=T*P';

Y_rec=T*diag(b)*C';%Y_residual=Y-Y_rec;

%%BringbackXandYtotheiroriginalunits%

Xori_rec=X_rec*diag(S_X)+(ones(n,1)*M_X);Yori_rec=Y_rec*diag(S_Y)+(ones(n,1)*M_Y);

%Unscaled_Y_hat=Yhat*diag(S_Y)+(ones(n,1)*M_Y);%TheWstartweightsgivesT=X*Wstar%

Wstar=W*inv(P'*W);B_pls=Wstar*diag(b)*C';

%%Bpls_starY=[1|1|X]*Bpls_star

%Bpls_star=[M_Y;[-M_X;eye(np,np)]*diag(S_X.^(-1))*B_pls*diag(S_Y)]Bpls_star=[[-M_X;eye(np,np)]*diag(S_X.^(-1))*B_pls*diag(S_Y)];Bpls_star(1,:)=Bpls_star(1,:)+M_Y;%%%%%%%%%%%%%Functions

Here%%%%%%%%%%%%%%%%%%%%%%%function[f]=normaliz(F);%USAGE:[f]=normaliz(F);

%normalizesendbackamatrixnormalizedbycolumn%(i.e.,eachcolumnvectorhasanormof1)[ni,nj]=size(F);

v=ones(1,nj)./sqrt(sum(F.^2));f=F*diag(v);

functionz=zscore(x);

%USAGEfunctionz=zscore(x);

%givesbackthez-normalizationforx

%ifXisamatrixZisnormalizedbycolumn%Z-scoresarecomputedwith

%samplestandarddeviation(i.e.N-1)%seezscorepop[ni,nj]=size(x);m=mean(x);s=std(x);

un=ones(ni,1);

z=(x-(un*m))./(un*s);应用例子

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%example_pls.m:PLSexample%RM3Fall2023

%November162023%

%Thisscriptshowshowtorun%aPartialleastsquareregression%(PLS).

%NeedPrograms:PLS_nipalsplotxyha%Theexampleisthe

%WineexamplefromAbdiH.(2023)%S/~herve

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clearclc;

disp(['ExampleofaPLSprogram.SeeAbdiH.(2023)']);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%************************************************************%%->Thisisyourtitle.

%%->Changeittofityourdataze_title=['PLS.Wines.'];

%%**********************************************************%%ThisisthedatamatrixofthePredictors(IV)%%->ChangeitforyourexampleX=[...

7713743147

105125167113133103];

%%%getthe#ofrowsand

columns%%%%%%%%%%%%%%%%%%%%%%%%%%[nI,nJ]=size(X);

%************************************************************

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%->Theseareyourpredictorsnames.%->Changethemtofityourdata

%YouneedasmanynamesasmcXhascolumnsn=0;

%

n=n+1;nom_x(n)={'Price'};n=n+1;nom_x(n)={'Sugar'};n=n+1;nom_x(n)={'Alcohol'};n=n+1;nom_x(n)={'Acidity'};

%%%Testthe#ofcolumsnamesifnJ~=n;

erreur(['Error->(Wrong#ofcolumnnames)!']);end

%%***********************************************************

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%->Theseareyourobservationsnames.%->Changethemtofityourdatal=0;

l=l+1;nom_r{l}={'W_1'};l=l+1;nom_r{l}={'W_2'};l=l+1;nom_r{l}={'W_3'};l=l+1;nom_r{l}={'W_4'};l=l+1;nom_r{l}={'W_5'};ifnI~=l;

erreur(['Error->(Wrong#ofrownames)!']);end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%