LDA人脸识别的matlab程序

1、以下是LDA的m文件函数: 你稍稍改改就能用了！% % %function eigvector, eigvalue, elapse = LDA(gnd,options,data) % LDA: Linear Discriminant Analysiseigvector, eigvalue = LDA(gnd, options, data)Input:data - Data matrix. Each row vector of fea is a data point.gnd - Colunm vector of the label information for each data point.

2、options - Struct value in Matlab. The fields in options that can be set:Regu - 1: regularized solution, a* = argmax%0: solve the sinularity problem bySVD%Default: 0%ReguAlpha -The regularization parameter.Valid%when Regu=1. Default value is0.1.%ReguType-'Ridge': Tikhonovregularization%'C

3、ustom': User provided%regularizationmatrix%Default: 'Ridge'%regularizerR- (nFea x nFea) regularization%matrix which should beprovided%if ReguType is 'Custom'.nFea is%the feature number of data%matrix(a'X'WXa)/(a'X'Xa+ReguAlpha*I)%Fisherface1:%nClass% % % principal

4、 %PCA% % % % % %step%PCARatio principle %exceed the%components).PCARatioPCARatio = nSmp -Default: 0The percentage ofcomponent kept in thestep. The percentage is calculated based on the eigenvalue. Default is 1 (100%, all the non-zero eigenvalues will be kept.If PCARatio > 1, the PCAwill keep exac

5、tlycomponents (does notexact number of non-zero% %new% % % % % % % %Examples:Output:eigvector - Each column is an embedding function, for aeigvalue elapsedata point (row vector) x, y = x*eigvector will be the embedding result of x.-The sorted eigvalue of LDA eigen-problem.-Time spent on different st

6、epsfea = rand(50,70);gnd = ones(10,1);ones(15,1)*2;ones(10,1)*3;ones(15,1)*4;options = 口；options.Fisherface = 1;eigvector, eigvalue = LDA(gnd, options, fea);Y = fea*eigvector;% See also LPP, constructW, LGE%Reference:% P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman, 掏 igenfaces% vs. fisherfaces

7、: recognition using class specific linear% projection, ? IEEE Transactions on Pattern Analysis and Machine% Intelligence, vol. 19, no. 7, pp. 711-720, July 1997. % Deng Cai, Xiaofei He, Yuxiao Hu, Jiawei Han, and Thomas Huang,% "Learning a Spatially Smooth Subspace for Face Recognition", C

8、VPR'2007% Deng Cai, Xiaofei He, Jiawei Han, "SRDA: An Efficient Algorithm for% Large Scale Discriminant Analysis", IEEE Transactions on Knowledge and% Data Engineering, 2007.%version 2.1 -June/2007%version 2.0 -May/2007%version 1.1 -Feb/2006%version 1.0 -April/2004% Written by Deng Cai

9、 (dengcai2 AT ) %if -exist('data',var,) global data;endif (-exist('options',var,) options =;endif isfield(options,'Regu') | options.RegubPCA = 1;if isfield(options,'PCARatio') options.PCARatio = 1;endelsebPCA = 0;if isfield(options,'ReguType') optio

10、ns.ReguType = 'Ridge'endif isfield(options,'ReguAlpha')options.ReguAlpha = 0.1;end endtmp_T = cputime;% = InitializationnSmp,nFea = size(data);if length(gnd) = nSmperror('gnd and data mismatch!');endclassLabel = unique(gnd);nClass = length(classLabel);Dim = nClass - 1;if bPCA

11、 & isfield(options,'Fisherface') & options.Fisherface options.PCARatio = nSmp - nClass;endif issparse(data)data = full(data);endsampleMean = mean(data,1);data = (data - repmat(sampleMean,nSmp,1);bChol = 0;if bPCA & (nSmp > nFea+1) & (options.PCARatio >= 1)DPrime = data&

12、#39;*data;DPrime = max(DPrime,DPrime');R,p = chol(DPrime);if p = 0bPCA = 0;bChol = 1;end end%=% SVD%=if bPCAif nSmp > nFeaddata = data'*data;ddata = max(ddata,ddata');eigvector_PCA, eigvalue_PCA = eig(ddata);eigvalue_PCA = diag(eigvalue_PCA);clear ddata;maxEigValue = max(abs(eigvalue_

13、PCA);eigIdx = find(eigvalue_PCA/maxEigValue < 1e-12);eigvalue_PCA(eigIdx)=;eigvector_PCA(:,eigIdx)=;junk, index = sort(-eigvalue_PCA);eigvalue_PCA = eigvalue_PCA(index);eigvector_PCA = eigvector_PCA(:, index);%=if options.PCARatio > 1idx = options.PCARatio;if idx < length(eigvalue_PCA)eigva

14、lue_PCA = eigvalue_PCA(1:idx);eigvector_PCA = eigvector_PCA(:,1:idx);endelseif options.PCARatio < 1sumEig = sum(eigvalue_PCA);sumEig = sumEig*options.PCARatio;sumNow = 0;for idx = 1:length(eigvalue_PCA)sumNow = sumNow + eigvalue_PCA(idx);if sumNow >= sumEigbreak;endendeigvalue_PCA = eigvalue_P

15、CA(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');eigvector, eigvalue_PCA = eig(ddata);eigvalue_PCA = diag(eigvalue_PCA);clear ddata;maxEigValue

16、 = 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);%=if options.PCARatio > 1idx = options.PCARatio;if idx < length(eigvalue_PCA)e

17、igvalue_PCA = eigvalue_PCA(1:idx);eigvector = eigvector(:,1:idx);endelseif options.PCARatio < 1sumEig = sum(eigvalue_PCA);sumEig = sumEig*options.PCARatio;sumNow = 0;for idx = 1:length(eigvalue_PCA)sumNow = sumNow + eigvalue_PCA(idx);if sumNow >= sumEigbreak;endendeigvalue_PCA = eigvalue_PCA(1

18、:idx);eigvector = eigvector(:,1:idx);end%=eigvalue_PCA = eigvalue_PCA.A-.5;eigvector_PCA = (data'*eigvector).*repmat(eigvalue_PCA',nFea,1);data = eigvector; clear eigvector;end elseif -bCholDPrime = data'*data;%options.ReguAlpha = nSmp*options.ReguAlpha;switch lower(options.ReguType) cas

19、e lower('Ridge')for i=1:size(DPrime,1)DPrime(i,i) = DPrime(i,i) + options.ReguAlpha; endcase lower('Tensor')DPrime = DPrime + options.ReguAlpha*options.regularizerR; case lower('Custom')DPrime = DPrime + options.ReguAlpha*options.regularizerR; otherwiseerror('ReguType doe

20、s not exist!'); endDPrime = max(DPrime,DPrime');end endnSmp,nFea = size(data);Hb = zeros(nClass,nFea);for i = 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

21、;if bPCAdumpVec,eigvalue,eigvector = svd(Hb,'econ');eigvalue = diag(eigvalue);eigIdx = find(eigvalue < 1e-3);eigvalue(eigldx)=;eigvector(:,eigldx)=;eigvalue = eigvalue.A2;eigvector =eigvector_PCA*(repmat(eigvalue_PCA,1,length(eigvalue).*eigvector); elseWPrime = Hb'*Hb;WPrime = max(WPr

22、ime,WPrime');dimMatrix = size(WPrime,2);if Dim > dimMatrixDim = dimMatrix;endif isfield(options,'bEigs')if options.bEigsbEigs = 1;elsebEigs = 0;endelseif (dimMatrix > 1000 & Dim < dimMatrix/10) | (dimMatrix > 500 & Dim< dimMatrix/20) | (dimMatrix > 250 & Dim < dimMat