ORL人脸数据库_人脸识别_ORL_matlab

% eigvector 特征向量 % eigvalue 特征值 % elapse 时间推移 function [eigvector, eigvalue, elapse] = PCA(data, options) %% PCA Principal Component Analysis % % Usage: % [eigvector, eigvalue] = PCA(data, options) % [eigvector, eigvalue] = PCA(data) % % Input: % data - Data matrix. Each row vector of fea is a data point. % % options.ReducedDim - The dimensionality of the reduced subspace. If 0, % all the dimensions will be kept. % Default is 0. % % 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 PCA eigen-problem. % % Examples: % fea = rand(7,10); % [eigvector,eigvalue] = PCA(fea,4); % Y = fea*eigvector; % % version 2.2 --Feb/2009 % 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) % %% 判断是否有选项（降维数） if (~exist('options','var')) options = []; end %% 给出降维数 ReducedDim = 0; if isfield(options,'ReducedDim') ReducedDim = options.ReducedDim; end %% 判断降维数是否合理0<ReducedDim<样本维数 [nSmp,nFea] = size(data); if (ReducedDim > nFea) || (ReducedDim <=0) ReducedDim = nFea; %如果大于维数活着小于等于0，就等于样本维数 end %% 计时，可以用tic/toc更准确 tmp_T = cputime; %% 如果稀疏矩阵的存储方式是sparse storage organization，则返回逻辑1；否则返回逻辑0 if issparse(data) data = full(data); %把稀疏矩阵转为全矩阵 end %% 样本去均值化 sampleMean = mean(data,1); %求样本每一列均值 data = (data - repmat(sampleMean,nSmp,1)); %去均值 %% if nFea/nSmp > 1.0713 % 维数／样本数 % This is an efficient method which computes the eigvectors of % of A*A^T (instead of A^T*A) first, and then convert them back to % the eigenvectors of A^T*A. ddata = data*data'; ddata = max(ddata, ddata'); %获取每一个元素最大 dimMatrix = size(ddata,2); %ddata的维数 if dimMatrix > 1000 && ReducedDim < dimMatrix/10 % using eigs to speed up! option = struct('disp',0); %d = eigs(A,k,sigma,opts) %返回k个最大特征值, %sigma取值：'lm' 表示绝对值最大的特征值；'sm' 绝对值最小特征值； %对实对称问题：'la'表示最大特征值；'sa'为最小特征值； %对非对称和复数问题：'lr' 表示最大实部；'sr' 表示最小实部； %'li' 表示最大虚部；'si'表示最小虚部 [eigvector, eigvalue] = eigs(ddata,ReducedDim,'la',option);%求特征向量 特征值 eigvalue = diag(eigvalue);%创建对角矩阵 else [eigvector, eigvalue] = eig(ddata); %直接算特征向量特征值 eigvalue = diag(eigvalue); %对角阵 [junk, index] = sort(-eigvalue); %junk排序好的向量index是索引-为了从大到小 eigvalue = eigvalue(index); eigvector = eigvector(:, index); %这两步重新排序 end clear ddata; maxEigValue = max(abs(eigvalue)); %abs绝对值，求最大特征值 eigIdx = find(abs(eigvalue)/maxEigValue < 1e-12); %获取很小的特征值 eigvalue (eigIdx) = []; %将对应的特征值置空 eigvector (:,eigIdx) = [];%将对应的特征向量置空 % 不懂 eigvector = data'*eigvector; % Eigenvectors of A^T*A eigvector = eigvector*diag(1./(sum(eigvector.^2).^0.5)); % Normalization else ddata = data'*data; ddata = max(ddata, ddata'); dimMatrix = size(ddata,2); if dimMatrix > 1000 & ReducedDim < dimMatrix/10 % using eigs to speed up! option = struct('disp',0); [eigvector, eigvalue] = eigs(ddata,ReducedDim,'la',option); eigvalue = diag(eigvalue); else [eigvector, eigvalue] = eig(ddata); eigvalue = diag(eigvalue); [junk, index] = sort(-eigvalue); eigvalue = eigvalue(index); eigvector = eigvector(:, index); end clear ddata; maxEigValue = max(abs(eigvalue)); eigIdx = find(abs(eigvalue)/maxEigValue < 1e-12); eigvalue (eigIdx) = []; eigvector (:,eigIdx) = []; end %% if ReducedDim < length(eigvalue) eigvalue = eigvalue(1:ReducedDim); eigvector = eigvector(:, 1:ReducedDim); end %% if isfield(options,'PCARatio') %PCA比 sumEig = sum(eigvalue); sumEig = sumEig*options.PCARatio; %特征值和X比例 sumNow = 0; for idx = 1:length(eigvalue) sumNow = sumNow + eigvalue(idx); if sumNow >= sumEig break; end end eigvector = eigvector(:,1:idx); end %% 计算花费的时间 elapse = cputime - tmp_T;