Matrix Coherence and the Nystrom Method

Ameet Talwalkar, Afshin Rostamizadeh
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:579-586, 2010.

Abstract

The Nystr\"{}om method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this assumption to the concept of matrix coherence, connecting coherence to the performance of the Nystr\"{}om method. Making use of related work in the compressed sensing and the matrix completion literature, we derive novel coherence-based bounds for the Nystr\"{}om method in the low-rank setting. We then present empirical results that corroborate these theoretical bounds. Finally, we present more general empirical results for the full-rank setting that convincingly demonstrate the ability of matrix coherence to measure the degree to which information can be extracted from a subset of columns.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-talwalkar10a, title = {Matrix Coherence and the Nystrom Method}, author = {Talwalkar, Ameet and Rostamizadeh, Afshin}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {579--586}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/talwalkar10a/talwalkar10a.pdf}, url = {https://proceedings.mlr.press/r8/talwalkar10a.html}, abstract = {The Nystr\"{}om method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this assumption to the concept of matrix coherence, connecting coherence to the performance of the Nystr\"{}om method. Making use of related work in the compressed sensing and the matrix completion literature, we derive novel coherence-based bounds for the Nystr\"{}om method in the low-rank setting. We then present empirical results that corroborate these theoretical bounds. Finally, we present more general empirical results for the full-rank setting that convincingly demonstrate the ability of matrix coherence to measure the degree to which information can be extracted from a subset of columns.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Matrix Coherence and the Nystrom Method %A Ameet Talwalkar %A Afshin Rostamizadeh %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-talwalkar10a %I PMLR %P 579--586 %U https://proceedings.mlr.press/r8/talwalkar10a.html %V R8 %X The Nystr\"{}om method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this assumption to the concept of matrix coherence, connecting coherence to the performance of the Nystr\"{}om method. Making use of related work in the compressed sensing and the matrix completion literature, we derive novel coherence-based bounds for the Nystr\"{}om method in the low-rank setting. We then present empirical results that corroborate these theoretical bounds. Finally, we present more general empirical results for the full-rank setting that convincingly demonstrate the ability of matrix coherence to measure the degree to which information can be extracted from a subset of columns. %Z Reissued by PMLR on 04 October 2026.
APA
Talwalkar, A. & Rostamizadeh, A.. (2010). Matrix Coherence and the Nystrom Method. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:579-586 Available from https://proceedings.mlr.press/r8/talwalkar10a.html. Reissued by PMLR on 04 October 2026.

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