Unsupervised Grouped Axial Data Modeling via Hierarchical Bayesian Nonparametric Models With Watson Distributions

Area of Science:

• Statistics
• Machine Learning
• Computational Biology

Background:

• Modeling grouped axial data presents challenges due to directional nature and potential for infinite components.
• Existing methods may lack flexibility in handling shared components across groups.

Purpose of the Study:

• To propose an unsupervised hierarchical nonparametric Bayesian framework for modeling grouped axial data.
• To develop flexible models based on mixtures of Watson distributions with shared infinite components.

Main Methods:

• Developed a hierarchical Pitman-Yor process mixture model for Watson distributions.
• Derived a hierarchical Dirichlet process mixture model by setting discount parameters to zero.
• Implemented a collapsed variational Bayes (CVB) inference algorithm with an annealing mechanism for model learning.

Main Results:

• Demonstrated the effectiveness of the proposed models on synthetic datasets.
• Successfully applied the framework to real-world problems, including gene expression data clustering and depth image analysis.
• The averaged collapsed variational Bayes inference strategy ensured convergence of the learning algorithm.

Conclusions:

• The proposed Bayesian framework offers a robust and flexible approach for unsupervised analysis of grouped axial data.
• The developed inference methods provide efficient and convergent learning for complex mixture models.
• The framework shows promise for applications in diverse fields requiring directional data analysis.