how to calculate eigen vector, value using in pca??

hello everyone.... my topic is face recognition... but problem is that how to calculate pca and how to find eigen value & matrix.. if anyone have an idea and have a matlab code for related this tropic please help me...

Answer 1

[Aashray]

Hello Pooja,

for performing PCA it is recommended to convert the images into greyscale to reduce the dimensionality.

Next, the covariance matrix can be found by directly using the MATLAB in-built function “cov”. This can then be used to find the eigen values and hence the principal components from the images.

You may refer to the following MATLAB code for more understanding:

% Load face images into a matrix (here X) where each column is a flattened image vector 
imageDir = './cats'; 
imageFiles = dir(fullfile(imageDir, '*.jpg')); 
numImages = length(imageFiles); 
sampleImage = imread(fullfile(imageDir, imageFiles(1).name)); 
[imageHeight, imageWidth] = size(rgb2gray(sampleImage)); % Convert to grayscale 

% I have used 100 images of size 64x64 for illustration, so X is 4096x100. 
X = zeros(imageHeight * imageWidth, numImages); 
for i = 1:numImages 
    img = imread(fullfile(imageDir, imageFiles(i).name)); 
    if size(img, 3) == 3 
        img = rgb2gray(img); 
    end 
    X(:, i) = img(:); 
end 

% Centering the data by subtracting the mean face 
mean_face = mean(X, 2); 
X_centered = X - mean_face; 

% Calculating the covariance matrix, and the eigenvectors and eigenvalues matrix 
cov_matrix = cov(X_centered'); 
[eigenvectors, eigenvalues_matrix] = eig(cov_matrix); 

% Extracting eigenvalues from the diagonal of the eigenvalues matrix 
eigenvalues = diag(eigenvalues_matrix); 

% Sorting eigenvalues in descending order, and the corresponding eigen vectors 
[sorted_eigenvalues, index] = sort(eigenvalues, 'descend'); 
sorted_eigenvectors = eigenvectors(:, index); 

k = 10; % Selecting the top k eigenvectors (as they represent the principal components) 
principal_components = sorted_eigenvectors(:, 1:k); 

The following links might be helpful for better understanding of “cov”, “eig”, and “diag” functions:

• https://www.mathworks.com/help/matlab/ref/cov.html
• https://www.mathworks.com/help/matlab/ref/eig.html
• https://www.mathworks.com/help/matlab/ref/diag.html

You can also refer to the attached output for better understanding, the principal components variable is highlighted: