Principal Component Analysis (PCA) to extract first two principal components from sample covariance matrix of X and project X onto those two components.

Hi everybody, I'm trying to solve this problem I'm facing to from several hours. I have 3 classes of images and for each class I have 72 pictures, totally 216 images. I have already read all the pixels of each image and I have defined the matrix containing all pixels, X (216x49152). My goal is to standardize X, use PCA to extract first two principal components from sample covariance matrix of X, project X onto those two components and finally make some scatter plot to make considerations.

The problem I found is that using princomp function I would need much more available memory. Thus I decided to compute the correlation matrix of the standardized version of X (sigma = X_std * X_std'). In fact, if the matrix is standardized computing the correlation matrix is equivalent to compute the coariance matrix (right??).

Anyway, applying the function PCACOV to sigma (correlation matrix) I get a squared matrix of PCA coefficients. How can I project my matrix onto the first 2 components?? How can I use a scatter-plot with dierent colors standing for different classes??

That's the code:

clear all

a = dir('*.png');

nfiles = length(a);

X = [];

%% Images acquisition

for i=1:216

    filename = a(i).name;      

    I = imread(filename,'png');     

    ImgVector = I(:);

    ImgVector = ImgVector';

    X(i,:) = ImgVector;

end

X_std = zscore(X);

sigma = X_std*X_std';

[COEFF] = pcacov(sigma);