Estimating Gaussian Mixture Densities with EM – A Tutorial

Expectation Maximization (EM) [4, 3, 6] is a numerical algorithm for the maximization of functions of several variables. There are several tutorial introductions to EM, including [8, 5, 2, 7]. These are excellent references for greater generality about EM, several good intuitions, and useful explanations. The purpose of this document is to explain in a more self-contained way how EM can solve a special but important problem, the estimation of the parameters of a mixture of Gaussians from a set of data points. Here is the outline of what follows: