Doubly Stochastic Normalization for Spectral Clustering

Ron Zass; Amnon Shashua

Doubly Stochastic Normalization for Spectral Clustering

Ron Zass, Amnon Shashua^*

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

30 Scopus citations

Abstract

In this paper we focus on the issue of normalization of the affinity matrix in spectral clustering. We show that the difference between N-cuts and Ratio-cuts is in the error measure being used (relative-entropy versus L₁ norm) in finding the closest doubly-stochastic matrix to the input affinity matrix. We then develop a scheme for finding the optimal, under Frobenius norm, doubly-stochastic approximation using Von-Neumann's successive projections lemma. The new normalization scheme is simple and efficient and provides superior clustering performance over many of the standardized tests.

Original language	English
Title of host publication	NIPS 2006
Subtitle of host publication	Proceedings of the 19th International Conference on Neural Information Processing Systems
Editors	Bernhard Scholkopf, John C. Platt, Thomas Hofmann
Publisher	MIT Press Journals
Pages	1569-1576
Number of pages	8
ISBN (Electronic)	0262195682, 9780262195683
State	Published - 2006
Event	19th International Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, Canada Duration: 4 Dec 2006 → 7 Dec 2006

Publication series

Name	NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems

Conference

Conference	19th International Conference on Neural Information Processing Systems, NIPS 2006
Country/Territory	Canada
City	Vancouver
Period	4/12/06 → 7/12/06

Bibliographical note

Publisher Copyright:
© NIPS 2006.All rights reserved

Cite this

Zass, R., & Shashua, A. (2006). Doubly Stochastic Normalization for Spectral Clustering. In B. Scholkopf, J. C. Platt, & T. Hofmann (Eds.), NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems (pp. 1569-1576). (NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems). MIT Press Journals.

Zass, Ron ; Shashua, Amnon. / Doubly Stochastic Normalization for Spectral Clustering. NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems. editor / Bernhard Scholkopf ; John C. Platt ; Thomas Hofmann. MIT Press Journals, 2006. pp. 1569-1576 (NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems).

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abstract = "In this paper we focus on the issue of normalization of the affinity matrix in spectral clustering. We show that the difference between N-cuts and Ratio-cuts is in the error measure being used (relative-entropy versus L1 norm) in finding the closest doubly-stochastic matrix to the input affinity matrix. We then develop a scheme for finding the optimal, under Frobenius norm, doubly-stochastic approximation using Von-Neumann's successive projections lemma. The new normalization scheme is simple and efficient and provides superior clustering performance over many of the standardized tests.",

author = "Ron Zass and Amnon Shashua",

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year = "2006",

language = "אנגלית",

series = "NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems",

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Zass, R & Shashua, A 2006, Doubly Stochastic Normalization for Spectral Clustering. in B Scholkopf, JC Platt & T Hofmann (eds), NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems. NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems, MIT Press Journals, pp. 1569-1576, 19th International Conference on Neural Information Processing Systems, NIPS 2006, Vancouver, Canada, 4/12/06.

Doubly Stochastic Normalization for Spectral Clustering. / Zass, Ron; Shashua, Amnon.
NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems. ed. / Bernhard Scholkopf; John C. Platt; Thomas Hofmann. MIT Press Journals, 2006. p. 1569-1576 (NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Doubly Stochastic Normalization for Spectral Clustering

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