  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.
