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lda.m
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lda.m
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%% Question 3) One-vs-all, original X
clear all;
close all;
clc;
load face.mat
k = 10;
c = cvpartition(l,'Kfold',k); % separate the index list, l, into k separations
accuracy = zeros(k,1);
label_number = max(l);
conf_matrix = zeros(label_number, label_number);
img_width = 56;
img_height = 46;
img_size = 520;
%number of eigenvector chosen
%numOfEigenvector = [1:2:467];
numOfEigenvector = 255;
%PCA or RAW DATA
PCA_FLAG = 1;
LDA_FLAG = 1;
SVM_FLAG = 0;
NN_FLAG = 1;
t_OAA = zeros(size(numOfEigenvector, 2));
accuracy_overall = zeros(size(numOfEigenvector, 2));
index = 1;
for pca = numOfEigenvector
if PCA_FLAG == 0
training_data = zeros(468, img_width*img_height, k);
training_label = zeros(468, 1, k);
test_data = zeros(52, img_width*img_height, k);
test_label = zeros(52, 1, k);
else
training_data = zeros(468, pca, k);
training_label = zeros(468, 1, k);
test_data = zeros(52, pca, k);
test_label = zeros(52, 1, k);
end
%crange = [0.0001, 0.001, 0.01, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 500, 1000, 2000];
%srange = [0.1, 0.2, 0.3, 0.4, 0.5];
crange = [1];
srange = [1000];
coef0 = [0];
%for boxConstraints = crange
for offset = coef0;
% loop through all k-folds
%j=1;
for j=1:k
%for j = 1
training_data_tmp = X(:, training(c, j))';
training_label(:, :, j) = l(:, training(c, j))';
test_data_tmp = X(:, test(c, j))';
test_label(:, :, j) = l(:, test(c, j))';
training_size = size(training_data_tmp, 1);
test_size = size(test_data_tmp, 1);
if PCA_FLAG == 1
A = (training_data_tmp'-repmat(mean(training_data_tmp', 2), [1, training_size]));
B = (test_data_tmp'-repmat(mean(test_data_tmp', 2), [1, test_size]));
S_alternative = A' * A / training_size; % data covariance matrix using 1/N*At*A
[V_alternative, D_alternative] = eig(S_alternative); % calculate V as the eigenvectors and D as eigenvalues (in D's diagonal)
V_alternative = A * V_alternative; % using 1/N*At*A gives same eigenvalues, and V = A*eigenvectors when using 1/N*At*A
%-Reconstruct training data-
%Normalize eigenvectors,
%vectors are fliped because it was ordered ascendingly
VNormalizedFlip = fliplr(normc(V_alternative));
eigenvectorChosen = VNormalizedFlip(:, 1:pca);
%High-dimentional data projects to low-dimention
training_data_tmp = A' * eigenvectorChosen;
test_data_tmp = B' * eigenvectorChosen;
end
if LDA_FLAG == 1
A = (training_data_tmp'-repmat(mean(training_data_tmp', 2), [1, training_size]));
B = (test_data_tmp'-repmat(mean(test_data_tmp', 2), [1, test_size]));
LDAModel = fitcdiscr(A', training_label(:,:,j));
% Obtaining Fisher eigenvectors and eigenvalues
[Vf, Df] = eig(LDAModel.BetweenSigma,LDAModel.Sigma);
% Calculating weights
Df = fliplr(diag(Df));
Vf = fliplr(Vf);
% Calculating fisher weights
W1f = A'*Vf;
W2f = B'*Vf;
training_data_tmp = W1f;
test_data_tmp = W2f;
end
training_data(:,:,j) = training_data_tmp;
test_data(:,:,j) = test_data_tmp;
end
% loop through all k-folds
%j=1;
if SVM_FLAG == 1
t_begin = cputime;
for j=1:k
%for j=1
prob = [];
for i=1:label_number
training_label_normalised = double(training_label(:,:,j)==i);
model = fitcsvm(training_data(:,:,j), training_label_normalised,...
'Standardize',true, 'KernelScale', 300, 'KernelFunction',...
'rbf', 'BoxConstraint', 5);
% model = fitcsvm(training_data(:,:,j), training_label_normalised,...
% 'Standardize',true,'KernelFunction','polynomial','PolynomialOrder', 3, 'KernelScale',...
% scale, 'BoxConstraint', boxConstraints);
[~, p] = predict(model, test_data(:,:,j));
prob = [prob, p(:, 2)];
end
% predict the class with the highest probability
[~,pred] = max(prob,[],2);
accuracy(j) = sum(pred == test_label(:,:,j)) ./ numel(test_label(:,:,j)); %# accuracy
conf_matrix = conf_matrix + confusionmat(test_label(:,:,j), pred); %# confusion matrix
end
t_OAA(index) = cputime - t_begin;
accuracy_overall(index) = sum (accuracy)/k;
% figure;
% imagesc(conf_matrix)
index = index + 1;
end
if NN_FLAG == 1
NNTimeArray = zeros(1,468);
for NNNumOfEigenvector = 255:255
t_begin = cputime;
for eachFold = 1:k
% NNTrainingData = X(:, training(c, eachFold));
% NNTestData = X(:, test(c, eachFold));
NNTrainingSize = training_size;
NNTestSize = label_number;
% NNImageMean = mean(NNTrainingData, 2); % mean image from training set
%
% NNTrainingImageA = (NNTrainingData-repmat(NNImageMean, [1, NNTrainingSize]));
% NNTestImageA = (NNTestData-repmat(NNImageMean, [1, NNTestSize]));
%
% NNS = NNTrainingImageA' * NNTrainingImageA / NNTrainingSize; % data covariance matrix using 1/N*At*A
% [NNV_temp, NND] = eig(NNS); % calculate V as the eigenvectors and D as eigenvalues (in D's diagonal)
%
% %Normalize eigenvectors,
% %vectors are fliped because it was ordered ascendingly
% NNVfliped = fliplr(NNV_temp);
% NNVChosen = NNVfliped(:, 1:NNNumOfEigenvector);
%
% %using 1/N*At*A gives same eigenvalues, and V = A*eigenvectors when using 1/N*At*A
% NNEigenvectorChosen = normc(NNTrainingImageA * NNVChosen);
%High-dimentional data projects to low-dimention
NNeigenProjection = training_data(:,:,eachFold)';
NNTestEigenProjection = test_data(:,:,eachFold)';
%error is stored in reconError[foldNum, imageIndex]
%Index of min error is stored in minIndex[foldNum, imageIndex]
for i = 1 : NNTestSize
[reconError(eachFold, i), minIndex(eachFold, i)] = min(sqrt(sum((repmat(NNTestEigenProjection(:,i),1,NNTrainingSize)-NNeigenProjection).^2)));
end
end
NNTimeArray(NNNumOfEigenvector) = cputime - t_begin;
%For each picture, there should be k pictures that belongs to it, where
%K is the number of fold
numOfCorrectRecog = 0;
for i = 1 : NNTestSize
recogIndex(:,i) = ceil(minIndex(:,i)/9);
for j = 1 : k
if recogIndex(j,i)==i
numOfCorrectRecog = numOfCorrectRecog + 1;
end
end
end
recongAccuracy(NNNumOfEigenvector) = numOfCorrectRecog / img_size;
end
end
end
end