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Grouped Spherical Data Modeling Through Hierarchical Nonparametric Bayesian Models and Its Application to fMRI Data

Wentao Fan, Lin Yang, Nizar Bouguila

IEEE Transactions on Neural Networks and Learning Systems

|September 29, 2022

Summary

We introduce a novel hierarchical Bayesian model for analyzing spherical data, utilizing von Mises-Fisher distributions. This advanced method effectively models grouped data, showing promise in applications like fMRI analysis.

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Area of Science:

Computational Statistics
Machine Learning
Bioinformatics

Background:

Spherical data modeling is crucial for applications like gene expression analysis, document categorization, and gesture recognition.
Existing methods may not adequately capture the complex structures within grouped spherical datasets.

Purpose of the Study:

To propose a novel hierarchical nonparametric Bayesian model for modeling grouped spherical data.
To utilize von Mises-Fisher (VMF) distributions within a hierarchical Pitman-Yor (HPY) process mixture model framework.

Main Methods:

Developed a hierarchical nonparametric Bayesian model using von Mises-Fisher distributions.
Employed the hierarchical Pitman-Yor (HPY) process mixture model for infinite shared components.
Utilized a closed-form optimization algorithm based on variational Bayes (VB) for model learning.

Main Results:

The proposed model effectively handles grouped spherical data with complex distributions.
Demonstrated the model's performance on both synthetic datasets and real-world resting-state fMRI data.
The hierarchical structure and VMF distributions capture heavy tails and skewness inherent in the data.

Conclusions:

The developed hierarchical Bayesian nonparametric model offers a powerful approach for grouped spherical data analysis.
The model shows significant potential for applications in bioinformatics and neuroimaging, such as fMRI data analysis.