function [eigvector, eigvalue, elapse] = 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.
% elapse - Time spent on different steps
%
%
% 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)
%
bGlobal = 0;
if ~exist('data','var')
bGlobal = 1;
global data;
end
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, elapse] = LGE(W, [], options, data);
else
options.ReguAlpha = options.ReguAlpha*sum(D)/length(D);
D = sparse(1:nSmp,1:nSmp,D,nSmp,nSmp);
if bGlobal & isfield(options,'keepMean') & options.keepMean
[eigvector, eigvalue, elapse] = LGE(W, D, options);
else
[eigvector, eigvalue, elapse] = LGE(W, D, options, data);
end
end
eigIdx = find(eigvalue < 1e-3);
eigvalue (eigIdx) = [];
eigvector(:,eigIdx) = [];
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