www.pudn.com > PCA.zip > PCA_Tutorial.m, change:2011-02-23,size:2221b

% prophet mohammed said [ALLAH will help any one helped his/her brother/sister] PBUH

%This code to apply PCA (Principal Component Analysis)
% for any information please send to engalaatharwat@hotmail.com
%Egypt - HICIT - +20106091638

% Remember that each column of the data matrix(input matrix) represent one image or pattern
% Note: the data here represent two classes
% Class 1: data(:,1:4)
% Class 2: data(:,5:8)

data = [1     1     2     0     7     6     7     8
3     2     3     3     4     5     5     4];

[r,c]=size(data);
% Compute the mean of the data matrix "The mean of each row"
m=mean(data')';
% Subtract the mean from each image [Centering the data]
d=data-repmat(m,1,c);

% Compute the covariance matrix (co)
co=d*d';

% Compute the eigen values and eigen vectors of the covariance matrix
[eigvector,eigvl]=eig(co);

% Sort the eigen vectors according to the eigen values
eigvalue = diag(eigvl);
[junk, index] = sort(-eigvalue);
eigvalue = eigvalue(index);
eigvector = eigvector(:, index);

% Compute the number of eigen values that greater than zero (you can select any threshold)
count1=0;
for i=1:size(eigvalue,1)
if(eigvalue(i)>0)
count1=count1+1;
end
end

% We can use all the eigen vectors but this method will increase the
% computation time and complixity
%vec=eigvector(:,:);

% And also we can use the eigen vectors that the corresponding eigen values is greater than zero(Threshold) and this method will decrease the
% computation time and complixity

vec=eigvector(:,1:count1);

% Compute the feature matrix (the space that will use it to project the testing image on it)
x=vec'*d;

% If you have test data do the following
t=[1;1]  % this test data is close to the first class
%Subtract the mean from the test data
t=t-m;
%Project the testing data on the space of the training data
t=vec'*t;

% Then if you want to know what is the class of this test data?  just use
% any classifier (In our case we used minimum distance classifier)
alldata=t';
alldata(2:size(x,2)+1,:)=x'
dist=pdist(alldata);
[a,b]=min(dist(:,1:size(x,2)))
% So, b determine the closest observation to test data;