Open Access
June 2009 Modal clustering in a class of product partition models
David B. Dahl
Bayesian Anal. 4(2): 243-264 (June 2009). DOI: 10.1214/09-BA409


This paper defines a class of univariate product partition models for which a novel deterministic search algorithm is guaranteed to find the maximum a posteriori (MAP) clustering or the maximum likelihood (ML) clustering. While the number of possible clusterings of $n$ items grows exponentially according to the Bell number, the proposed mode-finding algorithm exploits properties of the model to provide a search requiring only $n(n+1)$ computations. No Monte Carlo is involved. Thus, the algorithm finds the MAP or ML clustering for potentially tens of thousands of items, whereas it can only be approximated through a stochastic search. Integrating over the model parameters in a Dirichlet process mixture (DPM) model leads to a product partition model. A simulation study explores the quality of the clustering estimates despite departures from the assumptions. Finally, applications to three specific models --- clustering means, probabilities, and variances --- are used to illustrate the variety of applicable models and mode-finding algorithm.


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David B. Dahl. "Modal clustering in a class of product partition models." Bayesian Anal. 4 (2) 243 - 264, June 2009.


Published: June 2009
First available in Project Euclid: 22 June 2012

zbMATH: 1330.62248
MathSciNet: MR2507363
Digital Object Identifier: 10.1214/09-BA409

Keywords: Bayesian nonparametrics , Dirichlet process mixture model , maximum a posteriori clustering , maximum likelihood clustering , Model-based clustering , Product partition models

Rights: Copyright © 2009 International Society for Bayesian Analysis

Vol.4 • No. 2 • June 2009
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