Finite Mixtures of Canonical Fundamental Skew t-Distributions

TL;DR

This paper introduces a flexible finite mixture model using the canonical fundamental skew t-distribution, unifying previous skew t models and enabling exact EM algorithm implementation for clustering asymmetric, long-tailed data.

Contribution

It proposes a generalized mixture model with CFUST distributions, unifies restricted and unrestricted skew t models, and provides exact EM algorithm implementation with new analytical results.

Findings

Unified framework for skew t-distributions

Exact EM algorithm for CFUST mixtures

Improved clustering of asymmetric data

Abstract

This is an extended version of the paper Lee and McLachlan (2014b) with simulations and applications added. This paper introduces a finite mixture of canonical fundamental skew t (CFUST) distributions for a model-based approach to clustering where the clusters are asymmetric and possibly long-tailed (Lee and McLachlan, 2014b). The family of CFUST distributions includes the restricted multivariate skew t (rMST) and unrestricted multivariate skew t (uMST) distributions as special cases. In recent years, a few versions of the multivariate skew t (MST) model have been put forward, together with various EM-type algorithms for parameter estimation. These formulations adopted either a restricted or unrestricted characterization for their MST densities. In this paper, we examine a natural generalization of these developments, employing the CFUST distribution as the parametric family for the component distributions, and point out that the restricted and unrestricted characterizations can be unified under this general formulation. We show that an exact implementation of the EM algorithm can be achieved for the CFUST distribution and mixtures of this distribution, and present some new analytical results for a conditional expectation involved in the E-step.