LPP: Locality Preserving Projections matlab

function [eigvector, eigvalue] = LPP(W, options, data) % LPP: Locality Preserving Projections % % [eigvector, eigvalue] = LPP(W, options, data) % % Input: % data - Data matrix. Each row vector of fea is a data point. % W - Affinity matrix. You can either call "constructW" % to construct the W, or construct it by yourself. % options - Struct value in Matlab. The fields in options % that can be set: % % Please see LGE.m for other options. % % 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 LPP eigen-problem. % % % Examples: % % fea = rand(50,70); % options = []; % options.Metric = 'Euclidean'; % options.NeighborMode = 'KNN'; % options.k = 5; % options.WeightMode = 'HeatKernel'; % options.t = 5; % W = constructW(fea,options); % options.PCARatio = 0.99 % [eigvector, eigvalue] = LPP(W, options, fea); % Y = fea*eigvector; % % % fea = rand(50,70); % gnd = [ones(10,1);ones(15,1)*2;ones(10,1)*3;ones(15,1)*4]; % options = []; % options.Metric = 'Euclidean'; % options.NeighborMode = 'Supervised'; % options.gnd = gnd; % options.bLDA = 1; % W = constructW(fea,options); % options.PCARatio = 1; % [eigvector, eigvalue] = LPP(W, options, fea); % Y = fea*eigvector; % % % Note: After applying some simple algebra, the smallest eigenvalue problem: % data^T*L*data = \lemda data^T*D*data % is equivalent to the largest eigenvalue problem: % data^T*W*data = \beta data^T*D*data % where L=D-W; \lemda= 1 - \beta. % Thus, the smallest eigenvalue problem can be transformed to a largest % eigenvalue problem. Such tricks are adopted in this code for the % consideration of calculation precision of Matlab. % % % See also constructW, LGE % %Reference: % Xiaofei He, and Partha Niyogi, "Locality Preserving Projections" % Advances in Neural Information Processing Systems 16 (NIPS 2003), % Vancouver, Canada, 2003. % % Xiaofei He, Shuicheng Yan, Yuxiao Hu, Partha Niyogi, and Hong-Jiang % Zhang, "Face Recognition Using Laplacianfaces", IEEE PAMI, Vol. 27, No. % 3, Mar. 2005. % % Deng Cai, Xiaofei He and Jiawei Han, "Document Clustering Using % Locality Preserving Indexing" IEEE TKDE, Dec. 2005. % % Deng Cai, Xiaofei He and Jiawei Han, "Using Graph Model for Face Analysis", % Technical Report, UIUCDCS-R-2005-2636, UIUC, Sept. 2005 % % Xiaofei He, "Locality Preserving Projections" % PhD's thesis, Computer Science Department, The University of Chicago, % 2005. % % 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('options','var')) options = []; end [nSmp,nFea] = size(data); if size(W,1) ~= nSmp error('W and data mismatch!'); end %========================== % If data is too large, the following centering codes can be commented % options.keepMean = 1; %========================== if isfield(options,'keepMean') && options.keepMean ; else if issparse(data) data = full(data); end sampleMean = mean(data); data = (data - repmat(sampleMean,nSmp,1)); end %========================== D = full(sum(W,2)); if ~isfield(options,'Regu') || ~options.Regu DToPowerHalf = D.^.5; D_mhalf = DToPowerHalf.^-1; if nSmp < 5000 tmpD_mhalf = repmat(D_mhalf,1,nSmp); W = (tmpD_mhalf.*W).*tmpD_mhalf'; clear tmpD_mhalf; else [i_idx,j_idx,v_idx] = find(W); v1_idx = zeros(size(v_idx)); for i=1:length(v_idx) v1_idx(i) = v_idx(i)*D_mhalf(i_idx(i))*D_mhalf(j_idx(i)); end W = sparse(i_idx,j_idx,v1_idx); clear i_idx j_idx v_idx v1_idx end W = max(W,W'); data = repmat(DToPowerHalf,1,nFea).*data; [eigvector, eigvalue] = LGE(W, [], options, data); else options.ReguAlpha = options.ReguAlpha*sum(D)/length(D); D = sparse(1:nSmp,1:nSmp,D,nSmp,nSmp); [eigvector, eigvalue] = LGE(W, D, options, data); end eigIdx = find(eigvalue < 1e-3); eigvalue (eigIdx) = []; eigvector(:,eigIdx) = [];