Thesis Defence: Robust Model-based Clustering via Mixtures of Multivariate Pseudo-Voigt Distributions

Babak Fathollahi Dehkordi, supervised by Dr. Jeffrey Andrews, will defend their thesis titled “Robust Model-based Clustering via Mixtures of Multivariate Pseudo-Voigt Distributions” in partial fulfillment of the requirements for the degree of Master of Science in Mathematics.

An abstract for Babak Fathollahi Dehkordi’s thesis is included below.

Defences are open to all members of the campus community as well as the general public. Please email jeff.andrews@ubc.ca to receive the Zoom link for this defence.

Abstract

We propose a multivariate extension of the pseudo-Voigt profile—a weighted convex combination of Gaussian and Cauchy distributions—within a finite mixture modeling framework for robust model-based clustering and outlier detection. To ensure parsimony and coherence within clusters, shared location and scale parameters are imposed between the Gaussian and Cauchy components. Parameter estimation is carried out via an Expectation–Conditional Maximization algorithm, with latent variables facilitating efficient likelihood-based inference. The performance of the proposed model is evaluated through simulation studies and applications to real-world data. Comparisons with established robust models, including mixtures of contaminated normal distributions, are provided to illustrate the model’s clustering accuracy and outlier detection capabilities. The framework is shown to be particularly effective for data characterized by heavy-tailed behavior.