Probabilistic Clustering Using Maximal Matrix Norm Couplings

TL;DR

This paper introduces a new probabilistic clustering method based on maximal matrix norm couplings, formulated as a convex maximization problem, with practical algorithms and competitive experimental results.

Contribution

It presents a novel local information theoretic approach for probabilistic clustering with relaxations for solving an NP-hard optimization problem.

Findings

Competitive performance on benchmark datasets

Effective relaxations solved via gradient ascent and alternating maximization

Demonstrates potential for further research in probabilistic clustering

Abstract

In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global optimum. In order to algorithmically solve this optimization problem, we propose two relaxations that are solved via gradient ascent and alternating maximization. Experiments on the MSR Sentence Completion Challenge, MovieLens 100K, and Reuters21578 datasets demonstrate that our approach is competitive with existing techniques and worthy of further investigation.