Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions

• Activity Number: 51 - Recent Developments in Modeling High-Dimensional and Complex Data
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: SSC (Statistical Society of Canada)
• Author(s): Utkarsh Dang* and Michael Gallaugher and Ryan Browne and Paul McNicholas
• Companies: Binghamton University and McMaster University and University of Waterloo and McMaster University
• Keywords: model-based clustering; model-based classification; EM algorithm; MM algorithm; skewed distributions; mixture models

Abstract

Mixtures of multivariate power exponential (MPE) distributions have been previously shown to be competitive for clustering in comparison to other elliptical mixture distributions. Here, we introduce a novel formulation of a multivariate skewed power exponential distribution and mixtures thereof to combine the flexibility of the MPE distribution with the ability to model cluster-specific skewness. These mixtures are more robust to departures from normality and can model skewness, varying tail weight, and peakedness within clusters. For parameter estimation, a generalized expectation-maximization approach combining minorization-maximization and optimization based on accelerated line search algorithms on the Stiefel manifold is utilized. These mixtures are implemented both in the model-based clustering and classification frameworks. Both toy and benchmark data are used for illustration and comparison to other mixture families.