Axially Symmetric Data Clustering Through Dirichlet Process Mixture Models of Watson Distributions

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• Clustering axially symmetric data presents unique challenges.
• Existing methods may not adequately capture the nuances of directional data.
• Bayesian nonparametric approaches offer flexibility in model complexity.

Purpose of the Study:

• To develop a flexible Bayesian nonparametric framework for clustering axially symmetric data.
• To introduce the infinite Watson mixture model as a powerful tool for directional data analysis.
• To provide scalable inference algorithms for large datasets.

Main Methods:

• Extension of the finite Watson mixture model to its infinite counterpart using Dirichlet processes and a stick-breaking representation.
• Development of a coordinate ascent mean-field variational inference algorithm for parameter learning with closed-form solutions.
• Implementation of a stochastic variational inference algorithm using stochastic gradient ascent for handling massive datasets.

Main Results:

• The proposed infinite Watson mixture model effectively clusters simulated axially symmetric data.
• The developed inference algorithms provide efficient parameter estimation.
• Successful application to real-world gene expression data clustering demonstrates practical utility.

Conclusions:

• The Bayesian nonparametric framework with Watson distributions offers a robust and scalable solution for clustering axially symmetric data.
• The infinite Watson mixture model is a promising approach for analyzing directional data in various scientific domains.
• The proposed inference methods enable the analysis of large-scale datasets, including gene expression data.