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what is regularised kernel discriminant analysis ? and how is uesd for feature extraction?

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nirai selvi
nirai selvi 2015-10-6
编辑： Walter Roberson 2015-10-6
I=imread('H:\Capture.PNG');
% faceDetector = vision.CascadeObjectDetector();
% bbox = step(faceDetector,I);
% B=insertObjectAnnotation(I, 'rectangle', bbox, 'face');
imshow(I)
% title('detected faces');
% n=size(bbox,1);
% str_n=num2str(n);
% str=strcat('number of detected faces are', str_n);
% disp(str);
function [eigvector, eigvalue, elapse] = KDA(options,gnd,data)
% KDA: Kernel Discriminant Analysis
%
% [eigvector, eigvalue] = KDA(options, gnd, data)
%
% Input:
% data -
% if options.Kernel = 0
% Data matrix. Each row vector of fea is a data
% point.
% if options.Kernel = 1
% Kernel matrix.
%
% gnd - Colunm vector of the label information for each
% data point.
% options - Struct value in Matlab. The fields in options
% that can be set:
%
% Kernel - 1: data is actually the kernel matrix.
% 0: ordinary data matrix.
% Default: 0
%
% Regu - 1: regularized solution,
% a* = argmax (a'KWKa)/(a'KKa+ReguAlpha*I)
% 0: solve the sinularity problem by SVD
% Default: 0
%
% ReguAlpha - The regularization parameter. Valid
% when Regu==1. Default value is 0.1.
%
% Please see constructKernel.m for other Kernel options.
%
% Output:
% eigvector - Each column is an embedding function, for a new
% data point (row vector) x, y = K(x,:)*eigvector
% will be the embedding result of x.
% K(x,:) = [K(x1,x),K(x2,x),...K(xm,x)]
% eigvalue - The sorted eigvalue of LDA eigen-problem.
% elapse - Time spent on different steps
%
% Examples:
%
% fea = rand(50,70);
% gnd = [ones(10,1);ones(15,1)*2;ones(10,1)*3;ones(15,1)*4];
% options.KernelType = 'Gaussian';
% options.t = 1;
% [eigvector, eigvalue] = KDA(gnd, options, fea);
%
% feaTest = rand(3,10);
% Ktest = constructKernel(feaTest,fea,options)
% Y = Ktest*eigvector;
%
%
%
% See also KSR, KLPP, KGE
%
% NOTE:
% In paper [2], we present an efficient approach to solve the optimization
% problem in KDA. We named this approach as Kernel Spectral Regression
% (KSR). I strongly recommend using KSR instead of this KDA algorithm.
%
%Reference:
%
% [1] G. Baudat, F. Anouar, Generalized
% Discriminant Analysis Using a Kernel Approach", Neural Computation,
% 12:2385-2404, 2000.
%
% [2] Deng Cai, Xiaofei He, Jiawei Han, "Efficient Kernel Discriminant
% Analysis via Spectral Regression", Department of Computer Science
% Technical Report No. 2888, University of Illinois at Urbana-Champaign
% (UIUCDCS-R-2007-2888), August 2007.
%
%
% version 2.0 --August/2007
% version 1.0 --April/2005
%
% Written by Deng Cai (dengcai2 AT cs.uiuc.edu)
%
if ~exist('data','var')
global data;
end
if (~exist('options','var'))
options = [];
end
if ~isfield(options,'Regu') | ~options.Regu
bPCA = 1;
else
bPCA = 0;
if ~isfield(options,'ReguAlpha')
options.ReguAlpha = 0.01;
end
end
if isfield(options,'Kernel') & options.Kernel
K = data;
clear data;
K = max(K,K');
elapse.timeK = 0;
else
[K, elapse.timeK] = constructKernel(data,[],options);
end
tmp_T = cputime;
% ====== Initialization
nSmp = size(K,1);
if length(gnd) ~= nSmp
error('gnd and data mismatch!');
end
classLabel = unique(gnd);
nClass = length(classLabel);
Dim = nClass - 1;
K_orig = K;
sumK = sum(K,2);
H = repmat(sumK./nSmp,1,nSmp);
K = K - H - H' + sum(sumK)/(nSmp^2);
K = max(K,K');
clear H;
%======================================
% SVD
%======================================
if bPCA
[U,D] = eig(K);
D = diag(D);
maxEigValue = max(abs(D));
eigIdx = find(abs(D)/maxEigValue < 1e-6);
if length(eigIdx) < 1
[dump,eigIdx] = min(D);
end
D (eigIdx) = [];
U (:,eigIdx) = [];
elapse.timePCA = cputime - tmp_T;
tmp_T = cputime;
Hb = zeros(nClass,size(U,2));
for i = 1:nClass,
index = find(gnd==classLabel(i));
classMean = mean(U(index,:),1);
Hb (i,:) = sqrt(length(index))*classMean;
end
[dumpVec,eigvalue,eigvector] = svd(Hb,'econ');
eigvalue = diag(eigvalue);
if length(eigvalue) > Dim
eigvalue = eigvalue(1:Dim);
eigvector = eigvector(:,1:Dim);
end
eigvector = (U.*repmat((D.^-1)',nSmp,1))*eigvector;
else
Hb = zeros(nClass,nSmp);
for i = 1:nClass,
index = find(gnd==classLabel(i));
classMean = mean(K(index,:),1);
Hb (i,:) = sqrt(length(index))*classMean;
end
B = Hb'*Hb;
T = K*K;
elapse.timePCA = cputime - tmp_T;
tmp_T = cputime;
for i=1:size(T,1)
T(i,i) = T(i,i) + options.ReguAlpha;
end
B = double(B);
T = double(T);
B = max(B,B');
T = max(T,T');
option = struct('disp',0);
[eigvector, eigvalue] = eigs(B,T,Dim,'la',option);
eigvalue = diag(eigvalue);
end
tmpNorm = sqrt(sum((eigvector'*K_orig).*eigvector',2));
eigvector = eigvector./repmat(tmpNorm',size(eigvector,1),1);
elapse.timeMethod = cputime - tmp_T;
elapse.timeAll = elapse.timeK + elapse.timePCA + elapse.timeMethod;

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采纳的回答

Walter Roberson
Walter Roberson 2015-10-6
编辑：Walter Roberson 2015-10-6
The question in your title is not a MATLAB question. You are asking a question about an algorithm and how the algorithm can be used in theory. You need to read the paper about the algorithm. The reference is given in the comments:
% [1] G. Baudat, F. Anouar, Generalized
% Discriminant Analysis Using a Kernel Approach", Neural Computation,
% 12:2385-2404, 2000.

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