Understanding concept of Gaussian Mixture Models

Question

I\'m trying to understand GMM by reading the sources available online. I have achieved clustering using K-Means and was seeing how GMM would compare to K-means.

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Answer 1

You are right, there is the same insight behind clustering with K-Means or GMM. But as you mentionned Gaussian Mixtures take data covariances into account. To find the maximum likelihood parameters (or maximum a posteriori MAP) of the GMM statistical model, you need to use an iterative process called the EM algorithm. Each iteration is composed of a E-step (Expectation) and a M-step (Maximization) and repeat until convergence. After convergence you can easily estimate the membership probabilities of each data vectors for each cluster model.