lpp.m

LPP for matlab, Good code for you!

function [eigvector, eigvalue] = LPP(X, W, options)
% LPP: Locality Preserving Projections
%
%       [eigvector, eigvalue] = LPP(X, W, options)
% 
%             Input:
%               X       - 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:
%                     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+alpha*I) 
%                                     0: solve the sinularity problem by SVD 
%                                     Default: 1 
%
%                            alpha -  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
%                           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 = 1;
%       W = constructW(fea,options);
%       options.PCARatio = 0.99
%       [eigvector, eigvalue] = LPP(fea, W, options);
%       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(fea, W, options);
%       Y = fea*eigvector;
% 
% 
% Note: After applying some simple algebra, the smallest eigenvalue problem:
%				X^T*L*X = \lemda X^T*D*X
%      is equivalent to the largest eigenvalue problem:
%				X^T*W*X = \beta X^T*D*X
%		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.
%
%    Written by Deng Cai (dengcai2 AT cs.uiuc.edu), April/2004, Feb/2006,
%                                             May/2007

if (~exist('options','var'))
   options = [];
end


[nSmp,nFea] = size(X);
if size(W,1) ~= nSmp
    error('W and X mismatch!');
end


D = full(sum(W,2));
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');

%==========================
% If X is too large, the following centering codes can be commented
%==========================
if issparse(X)
    X = full(X);
end
sampleMean = mean(X);
X = (X - repmat(sampleMean,nSmp,1));
%==========================

X = repmat(DToPowerHalf,1,nFea).*X;

[eigvector, eigvalue] = LGE(X, W, [], options);

eigIdx = find(eigvalue < 1e-3);
eigvalue (eigIdx) = [];
eigvector(:,eigIdx) = [];