Approximation algorithms for tensor clustering

Authors:
Stefanie Jegelka;Suvrit Sra;Arindam Banerjee
Affiliations:
Max Planck Institute for Biological Cybernetics, Tübingen, Germany;Max Planck Institute for Biological Cybernetics, Tübingen, Germany;Univ. of Minnesota, Twin Cities, Minneapolis, MN
Venue:
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Year:
2009

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Abstract

We present the first (to our knowledge) approximation algorithm for tensor clustering--a powerful generalization to basic 1D clustering. Tensors are increasingly common in modern applications dealing with complex heterogeneous data and clustering them is a fundamental tool for data analysis and pattern discovery. Akin to their 1D cousins, common tensor clustering formulations are NP-hard to optimize. But, unlike the 1D case, no approximation algorithms seem to be known. We address this imbalance and build on recent co-clustering work to derive a tensor clustering algorithm with approximation guarantees, allowing metrics and divergences (e.g., Bregman) as objective functions. Therewith, we answer two open questions by Anagnostopoulos et al. (2008). Our analysis yields a constant approximation factor independent of data size; a worst-case example shows this factor to be tight for Euclidean co-clustering. However, empirically the approximation factor is observed to be conservative, so our method can also be used in practice.