Estimating Gaussian Mixture Models from Data with Missing Features
Daniel W. McMichael · 1996
Maximum likelihood #ML# #tting of Gaussian mixture models #GMMs# to feature data is most e#ciently handled by the EM algorithm #1, 2, 3, 4#. The EM algorithm is directly applicable to multivariate data in which all the features are always present, and there are no missing values. Unfortunately, missing values are common: caused either by random or systematic e#ects. This study presentsanovel algorithm for estimating the parameters of GMMs when there are random missing values. The approachisBayesian in the missing values and ML in the GMM parameters. The same model can be applied to heteroscedastic data, and to indirectly observable mixed Gaussian observations. 1. INTRODUCTION Conventionally, Gaussian mixture models are used to model the density of feature data for which there is no a priori parametric model. GMMs are highly #exible: with an in#- nite supply of components, they can model densities of arbitrary complexity. Their use has become widespread since the development of the EM...