ldaPknn.rar_KNN 人脸_knn matlab_lda人脸识别_人脸库

function [eigvector1, eigvalue] = LDA(gnd,options,data) % LDA: Linear Discriminant Analysis % % [eigvector, 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. % options - Struct value in Matlab. The fields in options % that can be set: % % Regu - 1: regularized solution, % a* = argmax (a'X'WXa)/(a'X'Xa+ReguAlpha*I) % 0: solve the sinularity problem by SVD % Default: 0 % % ReguAlpha - The regularization parameter. Valid % when Regu==1. Default value is 0.1. % % ReguType - 'Ridge': Tikhonov regularization % 'Custom': User provided % regularization matrix % Default: 'Ridge' % regularizerR - (nFea x nFea) regularization % matrix which should be provided % if ReguType is 'Custom'. nFea is % the feature number of data % matrix % Fisherface - 1: Fisherface approach % PCARatio = nSmp - nClass % Default: 0 % % PCARatio - The percentage of principal % component kept in the PCA % step. The percentage is % calculated based on the % eigenvalue. Default is 1 % (100%, all the non-zero % eigenvalues will be kept. % If PCARatio > 1, the PCA step % will keep exactly PCARatio principle % components (does not exceed the % exact number of non-zero components). % % % Output: % eigvector - Each column is an embedding function, for a new % data point (row vector) x, y = x*eigvector % will be the embedding result of x. % eigvalue - The sorted eigvalue of LDA eigen-problem. % elapse - Time spent on different steps % % Examples: % % fea = rand(50,70); % gnd = [ones(10,1);ones(15,1)*2;ones(10,1)*3;ones(15,1)*4]; % options = []; % options.dim=dim; % 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, �Eigenfaces % vs. fisherfaces: 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", CVPR'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 (dengcai2 AT cs.uiuc.edu) % if ~exist('data','var') global data; end if (~exist('options','var')) options = []; end if ~isfield(options,'Regu') | ~options.Regu bPCA = 1; if ~isfield(options,'PCARatio') options.PCARatio = 1; end else bPCA = 0; if ~isfield(options,'ReguType') options.ReguType = 'Ridge'; end if ~isfield(options,'ReguAlpha') options.ReguAlpha = 0.1; end end tmp_T = cputime; % ====== Initialization [nSmp,nFea] = size(data); if length(gnd) ~= nSmp error('gnd and data mismatch!'); end classLabel = unique(gnd); nClass = length(classLabel); % Dim = nClass - 2;%--------------------------------- if bPCA & isfield(options,'Fisherface') & options.Fisherface options.PCARatio = nSmp - nClass; end if issparse(data) data = full(data); end sampleMean = mean(data,1); data = (data - repmat(sampleMean,nSmp,1)); bChol = 0; if bPCA & (nSmp > nFea+1) & (options.PCARatio >= 1) DPrime = data'*data; DPrime = max(DPrime,DPrime'); [R,p] = chol(DPrime); if p == 0 bPCA = 0; bChol = 1; end end %====================================== % SVD %====================================== if bPCA if nSmp > nFea ddata = data'*data; ddata = max(ddata,ddata'); [eigvector_PCA, eigvalue_PCA] = eig(ddata); eigvalue_PCA = diag(eigvalue_PCA); clear ddata; 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 = eigvalue_PCA(index); eigvector_PCA = eigvector_PCA(:, index); %======================================= if options.PCARatio > 1 idx = options.PCARatio; if idx < length(eigvalue_PCA) eigvalue_PCA = eigvalue_PCA(1:idx); eigvector_PCA = eigvector_PCA(:,1:idx); end elseif options.PCARatio < 1 sumEig = sum(eigvalue_PCA); sumEig = sumEig*options.PCARatio; sumNow = 0; for idx = 1:length(eigvalue_PCA) sumNow = sumNow + eigvalue_PCA(idx); if sumNow >= sumEig break; end end eigvalue_PCA = eigvalue_PCA(1:idx); eigvector_PCA = eigvector_PCA(:,1:idx); end %======================================= eigvalue_PCA = eigvalue_PCA.^-.5; data = (data*eigvector_PCA).*repmat(eigvalue_PCA',nSmp,1); else ddata = data*data'; ddata = max(ddata,ddata'); [eigvector, eigvalue_PCA] = eig(ddata); eigvalue_PCA = diag(eigvalue_PCA); clear ddata; 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); %======================================= if options.PCARatio > 1 idx = options.PCARatio; if idx < length(eigvalue_PCA) eigvalue_PCA = eigvalue_PCA(1:idx); eigvector = eigvector(:,1:idx); end elseif options.PCARatio < 1 sumEig = sum(eigvalue_PCA); sumEig = sumEig*options.PCARatio; sumNow = 0; for idx = 1:length(eigvalue_PCA) sumNow = sumNow + eigvalue_PCA(idx); if sumNow >= sumEig break;