A new iterative initialization of EM algorithm for Gaussian mixture models A new iterative initialization of EM algorithm for Gaussian mixture models

Abstract

For d-dimensional random variable X with n samples, the probability distribution of a finite Gaussian mixture model can be expressed by a weighted sum of K components : P ( X | Θ ) = ∑ m = 1 K α m p m ( X | θ m ) , (1) where α*m is m-th mixing proportion, which must satisfy α**m > 0, m = 1, …, K and ∑ m = 1 K α m = 1. In (6-1)$Eq (1)$, θ**m = {μ**m, Σm} is the set of parameters of the m-th component, where μ**m and Σm denote the mean vector and covariance matrix of the m-th mixture component, respectively. p**m is the probability density function of the m*-th component: p m ( X | θ m ) = 1 ( 2