Approximation Algorithms for Bregman Co-clustering and Tensor Clustering

TL;DR

This paper introduces the first guaranteed approximation algorithms for Bregman co-clustering and tensor clustering, extending clustering theory beyond Euclidean spaces and demonstrating practical effectiveness through experiments.

Contribution

It provides the first known approximation algorithms for Bregman co-clustering and tensor clustering, and extends approximation guarantees to tensor clustering with arbitrary metrics.

Findings

First guaranteed algorithms for Bregman co-clustering and tensor clustering.

Approximation factor established for tensor clustering with arbitrary metrics.

Experimental results show practical impact of the proposed methods.

Abstract

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor clustering [8,34]. Like k-means, these more general problems also suffer from the NP-hardness of the associated optimization. Researchers have developed approximation algorithms of varying degrees of sophistication for k-means, k-medians, and more recently also for Bregman clustering [2]. However, there seem to be no approximation algorithms for Bregman co- and tensor clustering. In this paper we derive the first (to our knowledge) guaranteed methods for these increasingly important clustering settings. Going beyond Bregman divergences, we also prove an approximation factor for tensor clustering with arbitrary separable metrics. Through extensive experiments we evaluate the characteristics of our method, and show that it also has practical impact.