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Approximation Algorithms for Tensor Clustering

2009

Conference Paper

ei


We present the first (to our knowledge) approximation algo- rithm 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.

Author(s): Jegelka, S. and Sra, S. and Banerjee, A.
Book Title: Algorithmic Learning Theory: 20th International Conference
Pages: 368-383
Year: 2009
Month: October
Day: 0
Editors: Gavalda, R. , G. Lugosi, T. Zeugmann, S. Zilles
Publisher: Springer

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1007/978-3-642-04414-4_30
Event Name: ALT 2009
Event Place: Porto, Portugal

Address: Berlin, Germany
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5916,
  title = {Approximation Algorithms for Tensor Clustering},
  author = {Jegelka, S. and Sra, S. and Banerjee, A.},
  booktitle = {Algorithmic Learning Theory: 20th International Conference},
  pages = {368-383},
  editors = {Gavalda, R. , G. Lugosi, T. Zeugmann, S. Zilles},
  publisher = {Springer},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Berlin, Germany},
  month = oct,
  year = {2009},
  month_numeric = {10}
}