LDA人臉識別的matlab程序

1、%eigvector, eigvalue = LDA(gnd, options, data)以下是LDA的m文件函數(shù)：你稍稍改改就能用了！functioneigvector,eigvalue,elapse=LDA(gnd,options,data)%LDA:LinearDiscriminantAnalysis%Input:data-Datamatrix.Eachrowvectoroffeaisadatapoint.gnd-Colunmvectorofthelabelinformationforeachdatapoint.options-StructvalueinMatlab.Thefields

2、inoptionsthatcanbeset:Regu -%ReguAlpha-%ReguType%regularizerR%Fisherface%PCARatio%1: regularizedsolution,a*=argmax(a'X'WXa)/(a'X'Xa+ReguAlpha*I)0:solvethesinularityproblembySVDDefault:0Theregularizationparameter.ValidwhenRegu=1.Defaultvalueis0.1.-'Ridge':Tikhonovregularizatio

3、n'Custom':UserprovidedregularizationmatrixDefault:'Ridge'(nFeaxnFea)regularizationmatrixwhichshouldbeprovidedifReguTypeis'Custom'.nFeaisthefeaturenumberofdatamatrix-1:FisherfaceapproachPCARatio=nSmp-nClassDefault:0-ThepercentageofprincipalcomponentkeptinthePCAstep.Thepercenta

4、geiscalculatedbasedontheeigenvalue.Defaultis1(100%,allthenon-zeroeigenvalueswillbekept.IfPCARatio>1,thePCAstepwillkeepexactlyPCARatioprinciplecomponents(doesnotexceedtheexactnumberofnon-zerocomponents).%Output:eigvector-Eachcolumnisanembeddingfunction,foranewdatapoint(rowvector)x,y=x*eigvectorwil

5、lbetheembeddingresultofx.eigvalue-ThesortedeigvalueofLDAeigen-problem.elapse-TimespentondifferentstepsExamples:fea=rand(50,70);gnd=ones(10,1);ones(15,1)*2;ones(10,1)*3;ones(15,1)*4;options=;options.Fisherface=1;eigvector,eigvalue=LDA(gnd,options,fea);Y=fea*eigvector;%SeealsoLPP,constructW,LGE%Refere

6、nce:%P.N.Belhumeur,J.P.Hespanha,andD.J.Kriegman,摺igenfaces%vs.fisherfaces:recognitionusingclassspecificlinear%projection,?IEEETransactionsonPatternAnalysisandMachine%Intelligence,vol.19,no.7,pp.711-720,July1997.%DengCai,XiaofeiHe,YuxiaoHu,JiaweiHan,andThomasHuang,%"LearningaSpatiallySmoothSubsp

7、aceforFaceRecognition",CVPR'2007%DengCai,XiaofeiHe,JiaweiHan,"SRDA:AnEfficientAlgorithmfor%LargeScaleDiscriminantAnalysis",IEEETransactionsonKnowledgeand%DataEngineering,2007.%version2.1-June/2007%version2.0-May/2007%version1.1-Feb/2006%version1.0-April/2004%ifexist('data'

8、,'var')globaldata;endif(exist('options','va。)options=;endifisfield(options,'Regu')|options.RegubPCA=1;ifisfield(options,'PCARatio')options.PCARatio=1;endelsebPCA=0;ifisfield(options,'ReguType')options.ReguType='Ridge'endifisfield(options,'ReguA

9、lpha')options.ReguAlpha=0.1;endendtmp_T=cputime;%=InitializationnSmp,nFea=size(data);iflength(gnd)=nSmperror('gndanddatamismatch!');endclassLabel=unique(gnd);nClass=length(classLabel);Dim=nClass-1;ifbPCA&isfield(options,'Fisherface')&options.Fisherfaceoptions.PCARatio=nSm

10、p-nClass;endifissparse(data)data=full(data);endsampleMean=mean(data,1);data=(data-repmat(sampleMean,nSmp,1);bChol=0;ifbPCA&(nSmp>nFea+1)&(options.PCARatio>=1)DPrime=data'*data;DPrime=max(DPrime,DPrime');R,p=chol(DPrime);ifp=0bPCA=0;bChol=1;endend%=%SVD%=ifbPCAifnSmp>nFeaddat

11、a=data'*data;ddata=max(ddata,ddata');eigvector_PCA,eigvalue_PCA=eig(ddata);eigvalue_PCA=diag(eigvalue_PCA);clearddata;maxEigValue=max(abs(eigvalue_PCA);eigIdx=find(eigvalue_PCA/maxEigValue<1e-12);eigvalue_PCA(eigIdx)=;eigvector_PCA(:,eigIdx)=;junk,index=sort(-eigvalue_PCA);eigvalue_PCA=ei

12、gvalue_PCA(index);eigvector_PCA=eigvector_PCA(:,index);%=ifoptions.PCARatio>1idx=options.PCARatio;ifidx<length(eigvalue_PCA)eigvalue_PCA=eigvalue_PCA(1:idx);eigvector_PCA=eigvector_PCA(:,1:idx);endelseifoptions.PCARatio<1sumEig=sum(eigvalue_PCA);sumEig=sumEig*options.PCARatio;sumNow=0;forid

13、x=1:length(eigvalue_PCA)sumNow=sumNow+eigvalue_PCA(idx);ifsumNow>=sumEigbreak;endendeigvalue_PCA=eigvalue_PCA(1:idx);eigvector_PCA=eigvector_PCA(:,1:idx);end%=eigvalue_PCA=eigvalue_PCA.A-.5;data=(data*eigvector_PCA).*repmat(eigvalue_PCA',nSmp,1);elseddata=data*data'ddata=max(ddata,ddata&#

14、39;);eigvector,eigvalue_PCA=eig(ddata);eigvalue_PCA=diag(eigvalue_PCA);clearddata;maxEigValue=max(eigvalue_PCA);eigIdx=find(eigvalue_PCA/maxEigValue<1e-12);eigvalue_PCA(eigIdx)=;eigvector(:,eigIdx)=;junk,index=sort(-eigvalue_PCA);eigvalue_PCA=eigvalue_PCA(index);eigvector=eigvector(:,index);%=ifo

15、ptions.PCARatio>1idx=options.PCARatio;ifidx<length(eigvalue_PCA)eigvalue_PCA=eigvalue_PCA(1:idx);eigvector=eigvector(:,1:idx);endelseifoptions.PCARatio<1sumEig=sum(eigvalue_PCA);sumEig=sumEig*options.PCARatio;sumNow=0;foridx=1:length(eigvalue_PCA)sumNow=sumNow+eigvalue_PCA(idx);ifsumNow>

16、=sumEigbreak;endendeigvalue_PCA=eigvalue_PCA(1:idx);eigvector=eigvector(:,1:idx);end%=eigvalue_PCA=eigvalue_PCA.A-.5;eigvector_PCA=(data'*eigvector).*repmat(eigvalue_PCA',nFea,1);data=eigvector;cleareigvector;endelseifbCholDPrime=data'*data;%options.ReguAlpha=nSmp*options.ReguAlpha;switc

17、hlower(options.ReguType)caselower('Ridge')fori=1:size(DPrime,1)DPrime(i,i)=DPrime(i,i)+options.ReguAlpha;endcaselower('Tensor')DPrime=DPrime+options.ReguAlpha*options.regularizerR;caselower('Custom')DPrime=DPrime+options.ReguAlpha*options.regularizerR;otherwiseerror('Regu

18、Typedoesnotexist!');endDPrime=max(DPrime,DPrime');endendnSmp,nFea=size(data);Hb=zeros(nClass,nFea);fori=1:nClass,index=find(gnd=classLabel(i);classMean=mean(data(index,:),1);Hb(i,:)=sqrt(length(index)*classMean;endelapse.timeW=0;elapse.timePCA=cputime-tmp_T;tmp_T=cputime;ifbPCAdumpVec,eigval

19、ue,eigvector=svd(Hb,'econ');eigvalue=diag(eigvalue);eigIdx=find(eigvalue<1e-3);eigvalue(eigIdx)=;eigvector(:,eigIdx)=;eigvalue=eigvalue.A2;eigvector=eigvector_PCA*(repmat(eigvalue_PCA,1,length(eigvalue).*eigvector);elseWPrime=Hb'*Hb;WPrime=max(WPrime,WPrime');dimMatrix=size(WPrime,2);ifDim>dimMatrixDim=dimMatrix;endifisfield(options,'bEigs')ifoptions.bEigsbEigs=1;elsebEigs=0;endelseif(dimMatrix>1000&Dim<dimMatrix/10)|(dimMatrix>500&Dim<dimMatrix/20)|(dimMatrix>250&Dim<dimMatrix/30)bEigs=1