Probabilistic Clustering Using the Baum-Eagon Inequality

The paper introduces a framework for clustering data objects in a similarity-based context. The aim is to cluster objects into a given number of classes without imposing a hard partition, but allowing for a soft assignment of objects to clusters. Our approach uses the assumption that similarities reflect the likelihood of the objects to be in a same class in order to derive a probabilistic model for estimating the unknown cluster assignments. This leads to a polynomial optimization in probability domain, which is tackled by means of a result due to Baum and Eagon. Experiments on both synthetic and real standard datasets show the effectiveness of our approach.