LDA人脸识别的matlab程序

1、% % % % %Valid%0.1.%regularizati on% matrix%provided%nFea is%Fisherface1: Fisherface approachmatLDA以下是LDA的m文件函数: 你稍稍改改就能用了！fun cti on eigvector, eigvalue, elapse = LDA(g nd,opti on s,data) % LDA: Lin ear Discrim inant An alysis% % eigvector, eigvalue = LDA(gnd, options, data) %In put:data -Data matr

2、ix. Each row vector of fea is a data point.gnd -Colunm vector of the label in formatio n for each data point.options - Struct value in Matlab. The fields in options that can be set:%Regu 1: regularized soluti(a'X'WXa)/(aXXa+ReguAlpha*l)a* = argmax %SVD0: solve the sinu larity problem%byDefau

3、lt: 0ReguAlpha - The regularizati on parameter.whe n Regu=1. Default value isReguType 'Ridge': Tikh onov'Custom': User provided regularizati onDefault: 'Ridge' regularizerR (nFea x nF ea) regularizati on matrix which should beif ReguType is 'Custom,.the feature nu mber of

4、 data matrix%n ClassPCARatio = n Smp -Default: 0%prin cipal%PCAPCARatioThe perce ntage ofcomp onent kept in the%step%PCARatio prin ciple%exceed thestep. The perce ntage is calculated based on the eige nv alue. Default is 1 (100%, all the non-zero eige nv alues will be kept. If PCARatio > 1, the P

5、CAwill keep exactlycomp onents (does not%comp onen ts).%exact nu mber of non-zero%new% % % % %Output:eigvector - Each colu mn is an embedd ing function, fordata point (row vector) x, y = x*eigvector w川 be the embedd ing result of x.eigvalue -The sorted eigvalue of LDA eige n-problem.elapse -Time spe

6、 nt on diff ere nt steps% Examples:% % % % % % % %fea = ran d(50,70);gnd = on es(10,1);o nes(15,1)*2;o nes(10,1)*3;o nes(15,1)*4; opti ons =;opti on s.Fisherface = 1;eigvector, eigvalue = LDA(gnd, options, fea);Y = fea*eigvector;% See also LPP, con structW, LGE %Refere nee:% P. N. Belhumeur, J. P. H

7、espanha, and D. J. Kriegman, 掏 igenfaces% vs. fisherfaces: recog niti on using class specific lin ear% projection, ? IEEE Transactions on Pattern Analysis and Machine% Intelligenee, vol. 19, no. 7, pp. 711-720, July 1997.% Deng Cai, Xiaofei He, Yuxiao Hu, Jiawei Han, and Thomas Hua ng,% "Lear n

8、ing a Spatially Smooth Subspace for Face Recog niti on”， CVPR2007%De ng Cai, Xiaofei He, Jiawei Han, HSRDA: An Efficie nt Algorithm for%Large Scale Discrim inant An alysis", IEEE Tran sact ions on Kno wledgeand% Data Engin eeri ng, 2007.%version 2.1-Ju ne/2007%version 2.0-May/2007%version 1.1-F

9、eb/2006%version 1.0-April/2004% Writte n by Deng Cai (de ngcai2 AT )%if exist('data7var') global data;endif (exist('optio ns'/var') optio ns =;endif isfield(options,'Regu') | -options.Regu bPCA = 1;if isfield(optio ns, p CARatio*)optio ns.PCARatio = 1;endelsebP

10、CA = 0;if isfield(opti on s/ReguType*)opti on s.ReguType = 'Ridge1; endif isfield(opti on s/ReguAlpha*)opti on s.ReguAlpha = 0.1; endendtmp_T = cputime;% = In itializati onn Smp ,nF ea = size(data);if len gth(g nd) = n Smperror(*g nd and data mismatch!1)； end classLabel = uniq ue(g nd); n Class

11、= len gth(classLabel); Dim = n Class - 1;if bPCA & isfield(optio ns/Fisherface1) & opti on s.Fisherface opti on s.PCARatio = n Smp - n Class;end if issparse(data)data = full(data);endsampleMea n = mean( data,1);data = (data - repmat(sampleMea n,n Smp,1);bChol = 0;if bPCA & (n Smp > nF

12、ea+1) & (optio ns.PCARatio >= 1) DPrime = data'*data;DPrime = max(DPrimeQPrime,);R,p = chol(DPrime);if p = 0bPCA = 0;bChol = 1;endend%= %SVD%= if bPCAif n Smp > nFeaddata = data'*data;ddata = max(ddata,ddata');eigvector_PCA, eigvalue_PCA = eig(ddata); eigvalue_PCA =diag(eigvalu

13、e_PCA); clear ddata;maxEigValue = max(abs(eigvalue_PCA); eigldx = fin d(eigvalue_PCA/maxEigValue < 1e-12); eigvalue_PCA(eigldx)=; eigvector_PCA(:,eigldx)=;junk, in dex = sort(-eigvalue_PCA); eigvalue_PCA = eigvalue_PCA(i ndex); eigvector_PCA = eigvector_PCA:, i ndex);%=if options.PCARatio > 1i

14、dx = optio ns.PCARatio;if idx < Ie ngth(eigvalue_PCA)eigvalue_PCA = eigvalue_PCA(1 :idx);eigvector_PCA = eigvector_PCA(:,1 :idx);endelseif optio ns.PCARatio < 1sumEig = sum(eigvalue_PCA); sumEig = sumEig*options.PCARatio; sumNow = 0;for idx = 1 :le ngth(eigvalue_PCA) sumNow = sumNow + eigvalue

15、_PCA(idx); if sumNow >= 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); else ddata = data*data'ddata = max(ddata,ddata');eigvector, eigvalue_PCA =

16、 eig(ddata); eigvalue_PCA = diag(eigvalue_PCA);clear ddata;maxEigValue = max(eigvalue_PCA);eigldx = fin d(eigvalue_PCA/maxEigValue < 1e-12);eigvalue_PCA(eigldx)=;eigvector(:,eigldx)=;junk, in dex = sort(-eigvalue_PCA); eigvalue_PCA = eigvalue_PCA(i ndex); eigvector = eigvector(:, in dex);%=if opt

17、io ns.PCARatio > 1idx = optio ns.PCARatio;if idx < Ie ngth(eigvalue_PCA)eigvalue PCA = eigvalue_PCA(1 :idx); eigvector = eigvector(:,1 :idx);endelseif options.PCARatio < 1sumEig = sum(eigvalue_PCA);sumEig = sumEig*optio ns.PCARatio; sumNow = 0;for idx = 1 :le ngth(eigvalue_PCA)sumNow = sumN

18、ow + eigvalue_PCA(idx);if sumNow >= 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', nF ea,1);data = eigvector; clear eigvector;end elseif -bCholDPrime = d

19、ataf*data;%opti on s.ReguAlpha = n Smp*opti on s.ReguAlpha;switch lower(optio ns.ReguType) case lower(,Ridge,)for i=1 :size(DPrime,1)DPrime(i,i) = DPrime(iJ) + opti on s.ReguAlpha; end case lower(*Te nsor')DPrime = DPrime + opti on s.ReguAlpha*opti on s.regularizerR; case lower(,Custom,)DPrime =

20、 DPrime + opti on s.ReguAlpha*opti on s.regularizerR; otherwise error(fReguType does not exist!1); endDPrime = max(DPrimeJDPrime,)； end endn Smp ,nF ea = size(data);Hb = zeros( nClass, nF ea);for i = 1 :n Class,in dex = fin d(g nd=classLabel(i);classMea n = mea n(data(i ndex,:),1);Hb (i,:) = sqrt(le

21、 ngth(i ndex)*classMea n;endelapse.timeW = 0;elapse.timePCA = cputime - tmp_T;tmp_T = cputime;if bPCAdumpVec,eigvalue,eigvector = svd(Hb/ec on');eigvalue = diag(eigvalue); eigldx = fin d(eigvalue < 1e-3);eigvalue(eigldx)=; eigvector(:,eigldx)=;eigvalue = eigvalue.A2;eigvector =eigvector_PCA*(

22、repmat(eigvalue_PCA,1,le ngth(eigvalue).*eigvector); elseWPrime = Hb'*Hb;WPrime = max(WPrime,WPrime');dimMatrix = size(WPrime,2);if Dim > dimMatrixDim = dimMatrix;endif isfield(opti on s；bEigs')if opti on s.bEigsbEigs = 1;elsebEigs = 0;endelseif (dimMatrix > 1000 & Dim < dimMatrix/10) |