lab2.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%coursework: face recognition with eigenfaces

% need to replace with your own path
%addpath software;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Loading of the images: You need to replace the directory 
Imagestrain = loadImagesInDirectory ( 'images/training-set/23x28/');
[Imagestest, Identity] = loadTestImagesInDirectory ( 'images/testing-set/23x28/');



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Computation of the mean, the eigenvalues, amd the eigenfaces stored in the
%facespace:
ImagestrainSizes = size(Imagestrain);
Means = floor(mean(Imagestrain));
CenteredVectors = (Imagestrain - repmat(Means, ImagestrainSizes(1), 1));

CovarianceMatrix = cov(CenteredVectors);

[U, S, V] = svd(CenteredVectors);
Space = V(: , 1 : ImagestrainSizes(1))';
Eigenvalues = diag(S);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Display of the mean image:
MeanImage = uint8 (zeros(28, 23));
for k = 0:643
   MeanImage( mod (k,28)+1, floor(k/28)+1 ) = Means (1,k+1);
 
end
figure;
subplot (1, 1, 1);
imshow(MeanImage);
title('Mean Image');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Display of the 20 first eigenfaces : Write your code here

EigenFace = uint8 (zeros(28, 23));

figure;
for i = 1:20
    subplot(5,5,i);
    imshow(reshape(Space(i,:),[28,23]), []);
    title(['Eigenface- ',num2str(i)])
end
sgtitle('First 20 eigenfaces');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Projection of the two sets of images omto the face space:
Locationstrain=projectImages (Imagestrain, Means, Space);
Locationstest=projectImages (Imagestest, Means, Space);

Threshold =20;

TrainSizes=size(Locationstrain);
TestSizes = size(Locationstest);
Distances=zeros(TestSizes(1),TrainSizes(1));
%Distances contains for each test image, the distance to every train image.

for i=1:TestSizes(1),
    for j=1: TrainSizes(1),
        Sum=0;
        for k=1: Threshold,
   Sum=Sum+((Locationstrain(j,k)-Locationstest(i,k)).^2);
        end,
     Distances(i,j)=Sum;
    end,
end,

Values=zeros(TestSizes(1),TrainSizes(1));
Indices=zeros(TestSizes(1),TrainSizes(1));
for i=1:70,
[Values(i,:), Indices(i,:)] = sort(Distances(i,:));
end,


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Display of first 6 recognition results, image per image:
figure;
x=6;
y=2;
for i=1:6,
      Image = uint8 (zeros(28, 23));
      for k = 0:643
     Image( mod (k,28)+1, floor(k/28)+1 ) = Imagestest (i,k+1);
      end,
   subplot (x,y,2*i-1);
    imshow (Image);
    title('Image tested');
    
    Imagerec = uint8 (zeros(28, 23));
      for k = 0:643
     Imagerec( mod (k,28)+1, floor(k/28)+1 ) = Imagestrain ((Indices(i,1)),k+1);
      end,
     subplot (x,y,2*i);
imshow (Imagerec);
title(['Image recognised with ', num2str(Threshold), ' eigenfaces:',num2str((Indices(i,1))) ]);
end,



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%recognition rate compared to the number of test images: Write your code here to compute the recognition rate using top 20 eigenfaces.

% Initialising the rate for test set
rate = [];  

for i = 1: length(Imagestest(:,1))
    % Compare the train indices with test identity. If equals then rate = 1
    if ceil(Indices(i,1)/5) == Identity(i)
        rate(i) = 1;
    else 
        rate(i) = 0;
    end
end

% Overall Recognition rate using 20 eigenfaces for the images in the test set
recognitionRate = (sum(rate)/70) *100;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
%effect of threshold (i.e. number of eigenfaces):   
averageRR=zeros(1,20);
for t=1:40,
  Threshold =t;  
Distances=zeros(TestSizes(1),TrainSizes(1));

for i=1:TestSizes(1),
    for j=1: TrainSizes(1),
        Sum=0;
        for k=1: Threshold,
   Sum=Sum+((Locationstrain(j,k)-Locationstest(i,k)).^2);
        end,
     Distances(i,j)=Sum;
    end,
end,

Values=zeros(TestSizes(1),TrainSizes(1));
Indices=zeros(TestSizes(1),TrainSizes(1));
number_of_test_images=zeros(1,40);% Number of test images of one given person.%YY I modified here
for i=1:70,
number_of_test_images(1,Identity(1,i))= number_of_test_images(1,Identity(1,i))+1;%YY I modified here
[Values(i,:), Indices(i,:)] = sort(Distances(i,:));
end,

rec_rate = [];
for i = 1: length(Imagestest(:,1))
    % if the indices of train does not match with Identity in test then rate is 0.
    if ceil(Indices(i,1)/5) == Identity(i)
        rec_rate(i) = 1;
    else 
        rec_rate(i) = 0;
    end
end
recognition_rate = sum(rec_rate)/70 *100;
averageRR(1,t) = recognition_rate;

end,
figure;
plot(averageRR(1,:));
title('Recognition rate against the number of eigenfaces used');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%effect of K: You need to evaluate the effect of K in KNN and plot the recognition rate against K. Use 20 eigenfaces here.

TrainingLabels = []; % initialize the training labels 
for i = 1:40
    TrainingLabels = horzcat(TrainingLabels, repmat(i,1,5));
end

% Overall Recoginition Rate for different k values 
overall_recog_rate = [];


for k = 1:200 % iterating over k neighbours (i.e. from 1 to 200)
    %fit knn model to training data
    knn_model = fitcknn(Imagestrain, TrainingLabels, 'NumNeighbors', k,'BreakTies', 'nearest');
    knn_predict = predict(knn_model, Imagestest); % Prediction on the test data
    
    % Initalise recoginition rate for every k
    knn_recog_rate = [];  
    
    for i = 1:length(Imagestest(:,1))
        % Compare the predictions with identity of test image and predicted
        if ceil(Indices(i,1)/5) == knn_predict(i)
            knn_recog_rate(i) = 1;
        else
            knn_recog_rate(i) = 0;
        end
    end
    
    overall_recog_rate(k) = ((sum(knn_recog_rate)/70)*100);
end
figure
plot(1:200, overall_recog_rate);
xlabel('K'); ylabel('Recognition rate')
title('Recoginition rate against different k');