Optimal Bayesian clustering using non-negative matrix factorization

TL;DR

This paper introduces a novel method for Bayesian clustering that employs non-negative matrix factorization to derive optimal partitions from posterior similarity matrices, improving accuracy over existing methods.

Contribution

The paper presents a new NMF-based approach for estimating optimal Bayesian clustering partitions from posterior similarity matrices, enhancing inference quality.

Findings

NMF-based method outperforms popular alternatives in various scenarios.

The approach allows for both hard and soft clustering partitions.

Improved accuracy in identifying true data groupings.

Abstract

Bayesian model-based clustering is a widely applied procedure for discovering groups of related observations in a dataset. These approaches use Bayesian mixture models, estimated with MCMC, which provide posterior samples of the model parameters and clustering partition. While inference on model parameters is well established, inference on the clustering partition is less developed. A new method is developed for estimating the optimal partition from the pairwise posterior similarity matrix generated by a Bayesian cluster model. This approach uses non-negative matrix factorization (NMF) to provide a low-rank approximation to the similarity matrix. The factorization permits hard or soft partitions and is shown to perform better than several popular alternatives under a variety of penalty functions.