Can any one explain what is the exact difference between PCA and MPCA, and how to apply the MPCA ON face images

2014 11 20
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wikipidea defines the differance bet PCA and MPCA in single line "PCA Opertares on image of 100*100 in to 10,000*1, where MPCA opertares on same image in two mode as 100*1 and 100*1" what it means , and how to implenet this with the matlab. if any one has code or tutorial about the step of MPCA, please help me out.

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Ahmet Cecen
Ahmet Cecen 2014-11-20

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The very same page you copy pasted that explanation from has 2 decent references of a code and example.
http://en.wikipedia.org/wiki/Multilinear_principal_component_analysis
In short it means PCA would assume a 100x100 image is actually a single 10000 dimensional vector, treating each pixel as a dimension. In contrast MPCA first assumes that the same 100x100 image is actually 100 separate row vectors each having 100 dimensions (treating every column as a dimension). Then it does the inverse (second mode) and assume the image is 100 separate column vectors each having 100 dimensions (treating each row as a dimension). Its and iterative projection problem. Also check out one of the references in particular:
http://www.comm.toronto.edu/~kostas/Publications2008/pub/102.pdf
which has pretty good definitions and theory in my opinion.

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dhiraj dabi
dhiraj dabi 2014-11-20
Thanks for prompt answer to my question , as per the documents you have mentioned herehttp://www.comm.toronto.edu/~kostas/Publications2008/pub/102.pdf i have tried to devloped one matlab code for MPCA which is as below plese correct me if i am wrong somewhere
clear all;
close all;
clc;
[f p]=uigetfile('*.*','');
path=[p f];
Img=imread(path);
Img=rgb2gray(Img);
figure;
imshow(Img) title('Input Image') %% FaceNo=4;
IMat=[];
for i=1:FaceNo
s=num2str(i);
s=[ s '.jpg'];
imr=imread(s);
t = imresize(imr,[500 500]);
% t=imread(s);
t=rgb2gray(t);
figure,imshow(t);
IMat(:,:,i)=t;
end
IMat=uint8(IMat);
% image vector
[rw cl]=size(IMat(:,:,1));
for i=1:FaceNo
IVect(:,i)=reshape(IMat(:,:,i),rw*cl,1);
end
% mean image
IMean=mean(IVect,2);
IMean=uint8(IMean);
% substract mean image from image vector
mn=[];
for i=1:FaceNo
mn=[mn IMean];
end
IVMean=IVect-mn;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% calculate covariance matrix
CVMat=double(IVMean)'*double(IVMean);
% calculate eigen values and eigen vectors
[eigVal eigVec]=eig(CVMat); eigVec=single(IVMean)*eigVec;
eigFace=eigVec(:,end:-1:1);
figure;
for i=1:4
t=eigVec(:,i);
t=reshape(t,rw,cl);
t=uint8(t);
end
% face space projection
[r c]=size(IVMean);
Wt=zeros(c,FaceNo);
for i=1:c
Wt(i,:)=single(IVMean(:,i))'*eigVec;
end
please correct me if i have wring in any of the above step, if you have any code which has used the same algorithm, , them please send me the link , ii will be very helpful for me to compare with my code
end

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