Hi Najah,
To transform the means of the Gaussian Mixture Model (GMM) back from the PCA-transformed space to the original feature space, you need to perform an inverse transformation using the PCA coefficients. Here's how you can do it:
% Generate random data
MyMatrix = rand(2, height * width);
% Perform PCA
[COEFF, SCORE, latent, tsquared, explained, mu] = pca(MyMatrix');
% Fit Gaussian Mixture Model
options = statset('Display', 'final');
GMModel = fitgmdist(SCORE, 2, 'Options', options);
% Get the means in the PCA-transformed space
MeansPCA = GMModel.mu;
% Transform means back to the original space
MeansOriginal = MeansPCA * COEFF' + mu;
% Plot the results
hold on;
g = ezcontour(@(x, y) pdf(GMModel, [x y]), ...
[min(SCORE(:, 1)) max(SCORE(:, 1))], ...
[min(SCORE(:, 2)) max(SCORE(:, 2))]);
% Plot means in PCA space
plot(MeansPCA(:, 1), MeansPCA(:, 2), '+');
% Plot means in original space
plot(MeansOriginal(:, 1), MeansOriginal(:, 2), 'o');
hold off;
