Critical Lines in Symmetry of Mixture Models and its Application to Component Splitting

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

Bibtex Metadata Paper

Authors

Kenji Fukumizu, Shotaro Akaho, Shun-ichi Amari

Abstract

We show the existence of critical points as lines for the likelihood func- tion of mixture-type models. They are given by embedding of a critical point for models with less components. A sufficient condition that the critical line gives local maxima or saddle points is also derived. Based on this fact, a component-split method is proposed for a mixture of Gaus- sian components, and its effectiveness is verified through experiments.