Approximation Algorithms for Bregman Co-clustering and Tensor Clustering

In the past few years powerful generalizations to the Euclidean k-means problem have been made. Some examples include Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,17], and tensor clustering [8,30]. 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. Our experiments indicate that our results also have some practical impact.