TY - GEN
T1 - Doubly stochastic normalization for spectral clustering
AU - Zass, Ron
AU - Shashua, Amnon
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=78149281655&partnerID=8YFLogxK
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AN - SCOPUS:78149281655
SN - 9780262195683
T3 - Advances in Neural Information Processing Systems
SP - 1569
EP - 1576
BT - Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference
T2 - 20th Annual Conference on Neural Information Processing Systems, NIPS 2006
Y2 - 4 December 2006 through 7 December 2006
ER -