Fast spectral clustering via the Nyström method

Anna Choromanska, Tony Jebara, Hyungtae Kim, Mahesh Mohan, Claire Monteleoni

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We propose and analyze a fast spectral clustering algorithm with computational complexity linear in the number of data points that is directly applicable to large-scale datasets. The algorithm combines two powerful techniques in machine learning: spectral clustering algorithms and Nyström methods commonly used to obtain good quality low rank approximations of large matrices. The proposed algorithm applies the Nyström approximation to the graph Laplacian to perform clustering. We provide theoretical analysis of the performance of the algorithm and show the error bound it achieves and we discuss the conditions under which the algorithm performance is comparable to spectral clustering with the original graph Laplacian. We also present empirical results.

Original languageEnglish (US)
Title of host publicationAlgorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings
Pages367-381
Number of pages15
Volume8139 LNAI
DOIs
StatePublished - 2013
Event24th International Conference on Algorithmic Learning Theory, ALT 2013 - Singapore, Singapore
Duration: Oct 6 2013Oct 9 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8139 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other24th International Conference on Algorithmic Learning Theory, ALT 2013
CountrySingapore
CitySingapore
Period10/6/1310/9/13

Fingerprint

Spectral Clustering
Graph Laplacian
Clustering algorithms
Clustering Algorithm
Low-rank Approximation
Error Bounds
Learning systems
Computational complexity
Theoretical Analysis
Machine Learning
Computational Complexity
Clustering
Approximation

Keywords

  • error bounds
  • large-scale clustering
  • Nyström method
  • performance guarantees
  • sampling
  • sparsity
  • spectral clustering
  • unsupervised learning

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Choromanska, A., Jebara, T., Kim, H., Mohan, M., & Monteleoni, C. (2013). Fast spectral clustering via the Nyström method. In Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings (Vol. 8139 LNAI, pp. 367-381). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8139 LNAI). https://doi.org/10.1007/978-3-642-40935-6_26

Fast spectral clustering via the Nyström method. / Choromanska, Anna; Jebara, Tony; Kim, Hyungtae; Mohan, Mahesh; Monteleoni, Claire.

Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings. Vol. 8139 LNAI 2013. p. 367-381 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8139 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Choromanska, A, Jebara, T, Kim, H, Mohan, M & Monteleoni, C 2013, Fast spectral clustering via the Nyström method. in Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings. vol. 8139 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8139 LNAI, pp. 367-381, 24th International Conference on Algorithmic Learning Theory, ALT 2013, Singapore, Singapore, 10/6/13. https://doi.org/10.1007/978-3-642-40935-6_26
Choromanska A, Jebara T, Kim H, Mohan M, Monteleoni C. Fast spectral clustering via the Nyström method. In Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings. Vol. 8139 LNAI. 2013. p. 367-381. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-40935-6_26
Choromanska, Anna ; Jebara, Tony ; Kim, Hyungtae ; Mohan, Mahesh ; Monteleoni, Claire. / Fast spectral clustering via the Nyström method. Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings. Vol. 8139 LNAI 2013. pp. 367-381 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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