lsdasvm.rar_LSDA_lsda matlab_学习机 matlab_支持向量_降维方法

function [eigvector, eigvalue, elapse] = LGE(W, D, options, data) % LGE: Linear Graph Embedding % % [eigvector, eigvalue] = LGE(W, D, options, data) % % Input: % data - data matrix. Each row vector of data is a % sample vector. % W - Affinity graph matrix. % D - Constraint graph matrix. % LGE solves the optimization problem of % a* = argmax (a'data'WXa)/(a'data'DXa) % Default: D = I % % options - Struct value in Matlab. The fields in options % that can be set: % % ReducedDim - The dimensionality of the reduced % subspace. If 0, all the dimensions % will be kept. Default is 30. % % Regu - 1: regularized solution, % a* = argmax (a'X'WXa)/(a'X'DXa+ReguAlpha*I) % 0: solve the sinularity problem by SVD (PCA) % 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 % % 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 % sample vector (row vector) x, y = x*eigvector % will be the embedding result of x. % eigvalue - The sorted eigvalue of the eigen-problem. % elapse - Time spent on different steps % % % % Examples: % % See also LPP, NPE, IsoProjection, LSDA. % % %Reference: % % Deng Cai, Xiaofei He, Yuxiao Hu, Jiawei Han, and Thomas Huang, % "Learning a Spatially Smooth Subspace for Face Recognition", CVPR'2007 % % version 2.1 --June/2007 % version 2.0 --May/2007 % version 1.0 --Sep/2006 % % 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,'ReducedDim') Dim = options.ReducedDim; else Dim = 30; 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 bD = 1; if ~exist('D','var') | isempty(D) bD = 0; end [nSmp,nFea] = size(data); if size(W,1) ~= nSmp error('W and data mismatch!'); end if bD & (size(D,1) ~= nSmp) error('D and data mismatch!'); end tmp_T = cputime; bChol = 0; if bPCA & (nSmp > nFea) & (options.PCARatio >= 1) if bD DPrime = data'*D*data; else DPrime = data'*data; end if issparse(DPrime) DPrime = full(DPrime); end 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; if issparse(ddata) ddata = full(ddata); end 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 %======================================= if bD data = data*eigvector_PCA; else eigvalue_PCA = eigvalue_PCA.^-.5; data = (data*eigvector_PCA).*repmat(eigvalue_PCA',nSmp,1); end else ddata = data*data'; if issparse(ddata) ddata = full(ddata); end 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; end end eigvalue_PCA = eigvalue_PCA(1:idx); eigvector = eigvector(:,1:idx); end %======================================= eigvalue_PCA = eigvalue_PCA.^.5; eigvalue_PCAMinus = eigvalue_PCA.^-1; eigvector_PCA = (data'*eig