A generalized Bayes framework for probabilistic clustering

Area of Science:

• Statistics
• Machine Learning
• Data Mining

Background:

• Loss-based clustering (e.g., k-means) lacks uncertainty quantification.
• Model-based clustering faces computational challenges and kernel sensitivity.

Purpose of the Study:

• Propose a generalized Bayes framework for clustering.
• Bridge loss-based and model-based clustering paradigms.
• Introduce uncertainty quantification for clustering methods.

Main Methods:

• Utilize Gibbs posteriors for Bayesian updating with loss functions.
• Employ Bregman divergence and pairwise similarities for loss definitions.
• Develop deterministic and sampling algorithms for estimation and uncertainty quantification.

Main Results:

• The generalized Bayes framework accommodates various clustering algorithms, including k-means.
• Provides a method for quantifying uncertainty in cluster assignments.
• Enables calculation of data point clustering probabilities.

Conclusions:

• The proposed framework offers a coherent approach to Bayesian clustering.
• Enhances existing clustering methods by adding uncertainty quantification.
• Facilitates more reliable data grouping and interpretation.