olpp.m

OLPP for matlab, Good code for you!

function [eigvector, eigvalue, bSuccess] = OLPP(X, W, options)
% OLPP: Orthogonal Locality Preserving Projections
%
%       [eigvector, eigvalue, bSuccess] = OLPP(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 (PCA) 
%                                     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).  
%
%                            bDisp        -  0 or 1. diagnostic information
%                                            display
%
%             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 OLPP eigen-problem. 
%
%               bSuccess  - 0 or 1. Indicates whether the OLPP calcuation
%                           is successful. (OLPP needs matrix inverse,
%                           which will lead to eigen-decompose a
%                           non-symmetrical matrix. The caculation precsion
%                           of malab sometimes will cause imaginary numbers
%                           in eigenvectors. It seems that the caculation
%                           precsion of matlab is a little bit random, you
%                           can try again if not successful. More robust
%                           and efficient algorithms are welcome!) 
%                           
%                           
% 
% 
% 
%    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
%       options.ReducedDim = 5;
%       [eigvector, eigvalue, bSuccess] = OLPP(fea, W, options);
%       if bSuccess
%          Y = fea*eigvector;
%       end
%       
%       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;
%       options.ReducedDim = 5;
%       [eigvector, eigvalue, bSuccess] = OLPP(fea, W, options);
%       if bSuccess
%          Y = fea*eigvector;
%       end
%
% 
% 
% See also constructW, LPP, LGE, OLGE.
%
%Reference:
%
%   Deng Cai and Xiaofei He, "Orthogonal Locality Preserving Indexing" 
%   The 28th Annual International ACM SIGIR Conference (SIGIR'2005),
%   Salvador, Brazil, Aug. 2005.
%
%   Deng Cai, Xiaofei He, Jiawei Han and Hong-Jiang Zhang, "Orthogonal
%   Laplacianfaces for Face Recognition". IEEE Transactions on Image
%   Processing, vol. 15, no. 11, pp. 3608-3614, November, 2006.
% 
%    Written by Deng Cai (dengcai2 AT cs.uiuc.edu), August/2004, Feb/2006,
%                                                   Mar/2007, May/2007


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


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

D = sparse(1:nSmp,1:nSmp,sum(W),nSmp,nSmp);


%==========================
% 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));
%==========================


[eigvector, eigvalue, bSuccess] = OLGE(X, W, D, options);

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