Modal Clustering in a Univariate Class of Product Partition Models

This paper presents an algorithm for finding the maximum a posteriori (MAP) clustering in a class of univariate product partition models. While the number of possible clusterings of n observations grows according to the Bell exponential number, the dynamic programming algorithm presented here exploits properties of the model to provide an O(n2) search. Hence, the algorithm can be used to find the MAP clustering for tens of thousands of univariate data points, whereas previously it could only be approximated through a stochastic search. Integrating over the latent location variables in a Dirichlet Process mixture (DPM) model leads to a product partition model. The paper shows that several univariate, conjugate DPM mixture models satisfy the conditions for the mode-finding algorithm. The clustering algorithm is demonstrated with using data from a microarray experiment to detect differential gene expression involving 4,608 genes.