We present the first (to our knowledge) approximation algo- rithm for tensor clusteringa 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. |
| Links: | |
| 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 |
| BibTeX Type: | Conference Paper (inproceedings) |
| Address: | Berlin, Germany |
| DOI: | 10.1007/978-3-642-04414-4_30 |
| Event Name: | ALT 2009 |
| Event Place: | Porto, Portugal |
| Electronic Archiving: | grant_archive |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
BibTeX
@inproceedings{5916,
title = {Approximation Algorithms for Tensor Clustering},
booktitle = {Algorithmic Learning Theory: 20th International Conference},
abstract = {We present the first (to our knowledge) approximation algo-
rithm for tensor clusteringa 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.},
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},
author = {Jegelka, S. and Sra, S. and Banerjee, A.},
doi = {10.1007/978-3-642-04414-4_30},
month_numeric = {10}
}