Hy guys, I am fitting a Gaussian Mixture Model to high-dimensional data (40 dimensions) I have trained the model using EM, learned the parameters and now
I want to know quantitatively what is most important in capturing the structure of the data, the means or the covariance matrices. Currently, I can think of measuring the Euclidean distance between different means or the cosine of the principal eigenvectors of the different covariance matrices to measure if the direction of variability each covariance matrix captures is similar or different to the rest.

Any ideas ?