lsda.m

LSDA Code for matlab, Good code for you!

function [eigvector, eigvalue] = LSDA(X, gnd, options)
% LSDA: Locality Sensitive Discriminant Analysis
%
%       [eigvector, eigvalue] = LSDA(X, gnd, options)
% 
%             Input:
%               X       - Data matrix. Each row vector of fea is a data point.
%
%               gnd     - Label vector.  
%
%               options - Struct value in Matlab. The fields in options
%                         that can be set:
%                     k          = 0  
%                                     Wb:
%                                       Put an edge between two nodes if and
%                                       only if they belong to different classes. 
%                                     Ww:
%                                       Put an edge between two nodes if and
%                                       only if they belong to same class. 
%                                > 0
%                                     Wb:
%                                       Put an edge between two nodes if
%                                       they belong to different classes
%                                       and they are among the k nearst
%                                       neighbors of each other. 
%                                     Ww:
%                                       Put an edge between two nodes if
%                                       they belong to same class and they
%                                       are among the k nearst neighbors of
%                                       each other.  
%                     beta         [0,1] Paramter to tune the weight between
%                                        within-class graph and between-class
%                                        graph. Default 0.1. 
%                                        beta*L_b+(1-beta)*W_w 
%
%                     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 eigvalue of LPP eigen-problem. sorted from
%                           smallest to largest. 
% 
%
%    Examples:
%
%       
%       
%       fea = rand(50,70);
%       gnd = [ones(10,1);ones(15,1)*2;ones(10,1)*3;ones(15,1)*4];
%       options = [];
%       options.k = 5;
%       [eigvector, eigvalue] = LSDA(fea, gnd, options);
%       Y = fea*eigvector;
% 
% 
%
% See also LPP, LGE
%
%Reference:
%
%   Deng Cai, Xiaofei He, Kun Zhou, Jiawei Han and Hujun Bao, "Locality
%   Sensitive Discriminant Analysis", IJCAI'2007
%
%    Written by Deng Cai (dengcai2 AT cs.uiuc.edu), May/2006, May/2007


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


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

k = 0;
if isfield(options,'k') & (options.k < nSmp-1)
    k = options.k;
end


beta = 0.1;
if isfield(options,'beta') & (options.beta > 0) & (options.beta < 1)
    beta = options.beta;
end

Label = unique(gnd);
nLabel = length(Label);

Ww = zeros(nSmp,nSmp);
Wb = ones(nSmp,nSmp);
for idx=1:nLabel
    classIdx = find(gnd==Label(idx));
    Ww(classIdx,classIdx) = 1;
    Wb(classIdx,classIdx) = 0;
end

if k > 0
    D = EuDist2(X,[],0);
    [dump idx] = sort(D,2); % sort each row
    clear D dump
    idx = idx(:,1:options.k+1);
    
    G = sparse(repmat([1:nSmp]',[options.k+1,1]),idx(:),ones(prod(size(idx)),1),nSmp,nSmp);
    G = max(G,G');
    Ww = Ww.*G;
    Wb = Wb.*G;
    clear G
end


Wb = diag(sum(Wb,2)) - Wb;

D = full(sum(Ww,2));

Ww = sparse(beta*Wb+(1-beta)*Ww);
clear Wb

DToPowerHalf = D.^.5;
D_mhalf = DToPowerHalf.^-1;
tmpD_mhalf = repmat(D_mhalf,1,nSmp);
Ww = (tmpD_mhalf.*Ww).*tmpD_mhalf';
clear tmpD_mhalf;
Ww = max(Ww,Ww');

%==========================
% 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, Ww, [], options);

eigIdx = find(eigvalue < 1e-10);
eigvalue (eigIdx) = [];
eigvector(:,eigIdx) = [];