Modal Clustering in a Univariate Class of Product Partition Models

MODAL CLUSTERING IN A UNIVARIATE CLASS OFPRODUCT PARTITION MODELSDavid B. Dahldbdahl@stat.wisc.eduDepartment of Statistics, andDepartment of Biostatistics & Medical InformaticsUniversity of Wisconsin – MadisonNovember 3, 2003Technical Report #1085Department of StatisticsUniversity of Wisconsin – MadisonThe author wishes to thank his Ph.D. adviser Michael Newton for helpful advice and PhilippeBroet for access to data used in the example. The author is supported by the National Institutes ofHealth grant number EY07119. Software implementing the algorithm presented in this paper willbe available shortly athttp://www.stat.wisc.edu/˜dbdahl/modal/.MODAL CLUSTERING IN A UNIVARIATE CLASS OFPRODUCT PARTITION MODELSDavid B. DahlAbstractThis paper presents an algorithm for finding the maximum a posteriori (MAP) clusteringin a class of univariate product partition models. While the number of possible clusterings ofn observations grows according to the Bell exponential number, the dynamic programming2algorithm presented here exploits properties of the model to provide anO(n ) search. Hence,the algorithm can be used to find the MAP clustering for tens of thousands of univariate datapoints, whereas previously it could only be approximated through a stochastic search. Inte grating over the latent location variables in a Dirichlet Process mixture (DPM) model leadsto a product partition model. The paper shows that several univariate, conjugate DPM mix ture models ...