A “Density-Based” Algorithm for Cluster Analysis Using Species Sampling Gaussian Mixture Models

Abstract

We propose a new model for cluster analysis in a Bayesian nonparametric framework. Our model combines two ingredients, species sampling mixture models of Gaussian distributions on one hand, and a deterministic clustering procedure (DBSCAN) on the other. Here, two observations from the underlying species sampling mixture model share the same cluster if the distance between the densities corresponding to their latent parameters is smaller than a threshold; this yields a random partition which is coarser than the one induced by the species sampling mixture. Since this procedure depends on the value of the threshold, we suggest a strategy to fix it. In addition, we discuss implementation and applications of the model; comparison with more standard clustering algorithms will be given as well. Supplementary materials for the article are available online.

Key Words:

• Bayesian nonparametrics
• DBSCAN algorithm
• Dirichlet process

ACKNOWLEDGMENTS

The authors thank the two reviewers and the Editor for their valuable help in improving this article.