Beyond Affinity Propagation: Message Passing Algorithms for Clustering

Affinity propagation is an exemplar-based clustering method that takes as input similarities between data points. It outputs a set of data points that best represent the data (exemplars), and assignments of each non-exemplar point to its most appropriate exemplar, thereby partitioning the data set into clusters. The objective of affinity propagation is to maximize the sum of similarities between the data points and their exemplars. In this thesis, we develop several extensions of affinity propagation. The extensions provide clustering tools that go beyond the capabilities of the basic affinity propagation algorithm, and generalize it to various problems of interest in machine learning. We also investigate alternative approaches to the underlying mechanism of affinity propagation using recent inference techniques that are based on optimization theory. Affinity propagation was first described using a particular graphical model for the exemplar-based clustering problem. We first provide an alternative graphical model and derivation of affinity propagation, which are more amenable to model manipulation. Building on this representation, we develop capacitated affinity propagation, semi-supervised affinity propagation, and the hierarchical affinity propagation algorithms. We also discuss the relationship of affinity propagation to some canonical problems in combinatorial optimization. The underlying mechanism of affinity propagation is an approximate inference procedure known as max-product belief propagation. We provide a comparison of affinity propagation to alternative inference techniques such as max-product linear programming, and dual decomposition. We show that for a collection of benchmark data sets, affinity propagation outperforms these more theoretically justified approaches. We conclude by discussing the contributions and findings of this thesis, and how they relate to current research themes in more general inference problems. We point to several interesting avenues for future research.