Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions

Area of Science:

• Statistics
• Machine Learning
• Data Mining

Background:

• Mixtures of elliptical heavy-tailed distributions are increasingly used in clustering.
• Multivariate leptokurtic-normal (MLN) distributions offer advantages in parameter interpretability related to moments.

Purpose of the Study:

• To introduce and evaluate novel estimation procedures for mixtures of MLN distributions.
• To explore parsimonious forms of these mixtures and their fitting using the proposed algorithms.

Main Methods:

• Development of two estimation algorithms: one based on majorization-minimization (MM) and another on fixed-point approximation.
• Introduction of parsimonious parameterizations for MLN mixture models.
• Application of the estimation procedures to both simulated and real-world datasets.

Main Results:

• The proposed MM and fixed-point approximation algorithms provide effective methods for estimating MLN mixture models.
• Parsimonious models demonstrate utility in capturing complex data structures.
• Empirical investigations validate the performance of the models and algorithms across diverse datasets.

Conclusions:

• Mixtures of MLN distributions present a flexible and interpretable framework for clustering.
• The developed estimation algorithms enhance the practical applicability of these models.
• The study contributes robust statistical tools for advanced data analysis and pattern recognition.