Critical Lines in Symmetry of Mixture Models and its Application to Component Splitting
We show the existence of critical points as lines for the likelihood function 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 Gaussian components, and its effectiveness is verified through experiments.