Gaussian Mixture Models

Abstract

SynonymsGaussian mixture density; GMMDefinitionA Gaussian Mixture Model (GMM) is a parametric probability density function represented as a weighted sum of Gaussian component densities. GMMs are commonly used as a parametric model of the probability distribution of continuous measurements or features in a biometric system, such as vocal-tract related spectral features in a speaker recognition system. GMM parameters are estimated from training data using the iterative Expectation-Maximization (EM) algorithm or Maximum A Posteriori (MAP) estimation from a well-trained prior model.IntroductionA Gaussian mixture model is a weighted sum of M component Gaussian densities as given by the equation,(1)$$p({\bf x}\vert \lambda) = \sum \limits _{i=1}^{M}\;{{w_i}\;g({\bf x}\vert {\bf {\mu}}_{i},\, {\bf{\Sigma}}_{i}),}$$where x is a D-dimensional continuous-valued data vector (i.e. measurement or features), wi, i = 1, …, M, are the mixture weights, and