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One of the most used priors in Bayesian clustering is the Dirichlet prior. Itcan be expressed as a Chinese Restaurant Process. This process allowsnonparametric estimation of the number of clusters when partitioning datasets.Its key feature is the "rich-get-richer" property, which assumes a cluster hasan a priori probability to get chosen linearly dependent on population. In thispaper, we show that such prior is not always the best choice to model data. Wederive the Powered Chinese Restaurant process from a modified version of theDirichlet-Multinomial distribution to answer this problem. We then develop someof its fundamental properties (expected number of clusters, convergence).Unlike state-of-the-art efforts in this direction, this new formulation allowsfor direct control of the importance of the "rich-get-richer" prior.

Powered Dirichlet Process for Controlling the Importance of "Rich-Get-Richer" Prior Assumptions in Bayesian Clustering