Flexible Fitting and Diagnostics of Finite Mixture Models

• Activity Number: 376
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Guan Xing*+ and Ramani S. Pilla
• Companies: Case Western Reserve University and Case Western Reserve University
• Keywords: mixture model ; EM algorithm

Abstract

Mixture models, which can be viewed as clustering techniques, have become one of the most widely used statistical methods for the analysis of heterogeneous data. Mixture models enable flexible fitting of data arising from diverse fields such as astronomy, bioinformatics, genetics, hyperspectral imaging, medical imaging, and minefield detection. We first develop various functions for fitting the finite mixture models using the EM algorithm and the recent alternative EM methods we proposed. Moreover, a function for assessing the mixture fit based on the directional derivatives is proposed. The applicability and the flexibility of these simple and yet powerful functions is illustrated by fitting a finite mixture of normal distributions to the galaxy data. The proposed functions are quite general and allow fitting of mixtures of distributions from exponential families. The problem with starting values for the EM algorithm and an algorithmic termination criterion are also addressed. Model-building through the rotated, hierarchical, and composite EM algorithms and selection of the number of mixture components is illustrated through the galaxy dataset.