Transform points from PCA space to the original space!

Dears, I am using PCA to better represent my data so I could fit a gaussian distribution on them more easily. This is my code

MyMatrix=rand(2,hight*width); [COEFF,SCORE] = princomp(MyMatrix'); MyMatrix =SCORE';

 hold on

    options = statset('Display','final');
    GMModel = fitgmdist(MyMatrix',2,'Options',options);
    Means=GMModel.mu;

    g=ezcontour(@(x,y)pdf(GMModel,[x y]),[min(MyMatrix(1,:)) ...
    max(MyMatrix(1,:))],[min(MyMatrix(2,:)) max(MyMatrix(2,:))] );

    plot(Means(1,1),Means(1,2),'+');
    plot(Means(2,1),Means(2,2),'+');

hold off

Now I want to find the Means that I just calculated in the 2D original space, My question is : how to transform Means from the PCA coordinate space back to the original space.

I will appreciate any help! Thank you.

Answer 1

[Aditya]

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;