Doubly stochastic normalization for spectral clustering

Ron Zass*, Amnon Shashua

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

60 Scopus citations


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 L 1 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 languageAmerican English
Title of host publicationAdvances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference
Number of pages8
StatePublished - 2007
Event20th Annual Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, BC, Canada
Duration: 4 Dec 20067 Dec 2006

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference20th Annual Conference on Neural Information Processing Systems, NIPS 2006
CityVancouver, BC


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