Convex Relaxations of Bregman Divergence Clustering

TL;DR

This paper introduces a new class of convex relaxations for Bregman divergence clustering that are more flexible and scalable, leading to more accurate and tighter clustering results compared to existing methods.

Contribution

The authors propose a novel convex relaxation framework for Bregman divergence clustering that overcomes limitations of previous models and improves clustering quality and scalability.

Findings

New convex relaxations produce tighter clusterings.

Enhanced scalability through implicit matrix norm methods.

Improved clustering accuracy over state-of-the-art methods.

Abstract

Although many convex relaxations of clustering have been proposed in the past decade, current formulations remain restricted to spherical Gaussian or discriminative models and are susceptible to imbalanced clusters. To address these shortcomings, we propose a new class of convex relaxations that can be flexibly applied to more general forms of Bregman divergence clustering. By basing these new formulations on normalized equivalence relations we retain additional control on relaxation quality, which allows improvement in clustering quality. We furthermore develop optimization methods that improve scalability by exploiting recent implicit matrix norm methods. In practice, we find that the new formulations are able to efficiently produce tighter clusterings that improve the accuracy of state of the art methods.