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Can we use the Expectation Maximization algorithm for estimation of Gaussian Mixture Model with full covariance matrices?

If yes then can you please give me a reference paper? So far all the machine learning books I have consulted describes the estimation of only the diagonal covariance matrices.

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  • $\begingroup$ Please, do not use uppercase unless necessary. For acronyms as EM and GMM, it can be justified (although it would be better to use the actual entire terms), but FULL COVARIANCE and DIAGONAL COVARIANCE need not be uppercased ! To emphasize sommething, use italic (as in _italic_) or bold (as in **bold**). $\endgroup$ – Pece Aug 21 '14 at 9:31
  • $\begingroup$ This might be helpful en.wikipedia.org/wiki/… $\endgroup$ – VicP Aug 21 '14 at 15:51
  • $\begingroup$ It is estimating only the diagonal of covariance matrix, I need to estimate the full covariance matrix. $\endgroup$ – Najeeb Aug 22 '14 at 1:18
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If you are using python, all you need to do is add a parameter, covariance_type='full'.

For example,

m = mixture.GMM(n_components=3,covariance_type='diag')

Works for me.

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