Bayesian Clustering via Fusing of Localized Densities.

Area of Science:

• Computational statistics
• Machine learning
• Data mining

Background:

• Bayesian clustering commonly uses mixture models and Markov chain Monte Carlo (MCMC) algorithms.
• Existing methods are sensitive to kernel misspecification, potentially fragmenting true clusters.
• Gaussian kernels, when misapplied to non-Gaussian data, can lead to inaccurate cluster assignments.

Purpose of the Study:

• To develop a robust Bayesian clustering method that addresses kernel misspecification.
• To introduce Fusing of Localized Densities (FOLD) as a novel approach to meld mixture components.
• To provide a theoretically justified method with uncertainty quantification.

Main Methods:

• Developed Fusing of Localized Densities (FOLD), a novel Bayesian clustering technique.
• Utilized the posterior of mixture kernels to fuse components, enhancing robustness.
• Integrated FOLD as an add-on to existing MCMC algorithms for mixture models.

Main Results:

• FOLD demonstrates theoretical optimality under kernel misspecification.
• The method successfully melds components, leading to fewer, more meaningful clusters.
• Experiments show FOLD outperforms competing methods on simulated and real-world data.

Conclusions:

• FOLD offers a principled Bayesian approach to clustering, mitigating issues from kernel misspecification.
• The method provides uncertainty quantification and favors parsimonious cluster solutions.
• FOLD enhances the reliability of Bayesian mixture modeling for data clustering.