Robust mixture modelling using multivariate t-distribution with missing information

摘要

Modelling mixtures of multivariate t-distributions are usually used instead of Gaussian mixture models as a robust approach, when one fits a set of continuous multivariate data which have wider tail than Gaussian's or atypical observations. Further, the multivariate data set often involves missing values, which cannot be circumvented and then the missing values must be handled properly. In this paper, we present a framework for fitting mixtures of multivariate t-distributions when data are missing at random on the basis of maximum likelihood estimation. We resort to EM algorithm both for the estimation of mixture components and for coping with missing values. The iterative algorithm obtained can be applied to an extensive range of unsupervised clustering as well as supervised discrimination.