86bd78ab6679.m

%load the file containing images
load ('FaceData');
%create Training_ matriX
Training_matrix=[];
for i=1:40
 for j=1:5
H=FaceData(i,j).Image;
H=double(H)/255;
%find the dim of image
[m n]=size(H);
%convert the Image in to a column vector
H=reshape(H,m*n,1);
Training_matrix=horzcat(Training_matrix,H);

end
end 
%create Test matrix
Test_matrix=[];
for i=1:40
    for j=6:10
        H=FaceData(i,j).Image;
        H=reshape(H,m*n,1);
        Test_matrix=horzcat(Test_matrix,H);
    end
end
%Find the covariance of the training Matrix(C)
C= cov(Training_matrix');
%calculate the eigen vectors and eigen values of Covariance matrix c
[eigVec, eigVal] = eig(C);
%select the eigen vectors
R=[];
    i=1;
    for j=1:size(eigVal,1)
        R(i,1)=eigVal(j,j);
        R(i,2)=j;
        
        i=i+1;
    end
    
    R=sortrows(R,1);

    %Initialize the Transformation Matrix
    transform_matrix=[];
     
    M=2000;
    if( M > size(R,1) )
        %M=size(R,1);
    end
    
   % Select K eigenvectors, u1; u1; u3; : : : uK
    for j=size(R,1):-1: (size(R,1)-M + 1)
        transform_matrix=horzcat( transform_matrix , eigVec(:,R(j,2))  );
    end
%project the image or extract the feature vector
pca_project=[];
for i=1:200;
    pca_project(:,i)=transform_matrix'*Training_matrix(:,i);
end
%ploting the first 20 eigen faces
 figure;
 eigenface=[];
    for j=1:20
    eigenface=reshape(transform_matrix(:,j),56,46);
    subplot(4,5,j);
    imshow(eigenface,[]);
end
%reconstruction of the face image with the ff eigen vectors
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 Test_Feature_Vector=[];
    F=[2, 5, 10, 20, 40, 60, 100, 150, 200, 300,400, 500, 1000, 2000];
    
    figure;
    Image=Training_matrix(:,20);
    for j=1: size(F,2)
        P=transform_matrix(:,1:F(j));
        G=transpose(P) * Image;
        I=P * G;
        subplot(3,5,j);
        imshow( reshape(I,56,46) , []);
        title(num2str(F(j)) );
    end
    subplot(3,5,15);
    imshow( reshape(Image,56,46) , []);
    title(num2str('original') );
    figure;
Rank1_IdentificationRate=[];

for j=1: size(F,2)
    counter=0;
    Matrix=transform_matrix(:,1:F(j));
    
    Test_Feature_Vector= Matrix' *double(Test_matrix)/255;
    Training_Feature_Vector= Matrix' * Training_matrix;
    
    for n=1:size(Test_Feature_Vector,2)
        Eculidian_Distance=[];
        Total_Distance=0;
        for k=1:size(Training_Feature_Vector,2)           
            d=0;
            for i=1:size(Training_Feature_Vector,1)
                d=d + ( (Training_Feature_Vector(i,k)-Test_Feature_Vector(i,n)) .^ 2 );
            end
   
            d=sqrt(d);
            Eculidian_Distance(k)=d;
            Total_Distance=Total_Distance + d;
        end

        [Eculidian_Distance Index]=sort(Eculidian_Distance);

        if ceil(Index(1)/5)== ceil(n/5)
            counter=counter+1;
        end
    end
    Rank1_IdentificationRate(j)=counter/size(Test_Feature_Vector,2) ;
end

plot(F, Rank1_IdentificationRate)
title('Rank 1 identification rate');
xlabel('Number of feature vectors')
ylabel('Identification rate')