Fast Approximate Spectral Clustering for Dynamic Networks

Lionel Martin, Andreas Loukas, Pierre Vandergheynst
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:3423-3432, 2018.

Abstract

Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by a polynomial-based randomized sketching technique. We show that the proposed algorithm achieves clustering assignments with quality approximating that of spectral clustering and that it can yield significant complexity benefits when the graph dynamics are appropriately bounded. In our experiments, our method clusters 30k node graphs 3.9$\times$ faster in average and deviates from the correct assignment by less than 0.1%.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-martin18a, title = {Fast Approximate Spectral Clustering for Dynamic Networks}, author = {Martin, Lionel and Loukas, Andreas and Vandergheynst, Pierre}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {3423--3432}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/martin18a/martin18a.pdf}, url = {https://proceedings.mlr.press/v80/martin18a.html}, abstract = {Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by a polynomial-based randomized sketching technique. We show that the proposed algorithm achieves clustering assignments with quality approximating that of spectral clustering and that it can yield significant complexity benefits when the graph dynamics are appropriately bounded. In our experiments, our method clusters 30k node graphs 3.9$\times$ faster in average and deviates from the correct assignment by less than 0.1%.} }
Endnote
%0 Conference Paper %T Fast Approximate Spectral Clustering for Dynamic Networks %A Lionel Martin %A Andreas Loukas %A Pierre Vandergheynst %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-martin18a %I PMLR %P 3423--3432 %U https://proceedings.mlr.press/v80/martin18a.html %V 80 %X Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by a polynomial-based randomized sketching technique. We show that the proposed algorithm achieves clustering assignments with quality approximating that of spectral clustering and that it can yield significant complexity benefits when the graph dynamics are appropriately bounded. In our experiments, our method clusters 30k node graphs 3.9$\times$ faster in average and deviates from the correct assignment by less than 0.1%.
APA
Martin, L., Loukas, A. & Vandergheynst, P.. (2018). Fast Approximate Spectral Clustering for Dynamic Networks. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:3423-3432 Available from https://proceedings.mlr.press/v80/martin18a.html.

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