A unifying approach to hard and probabilistic clustering

Ron Zass; Amnon Shashua

doi:10.1109/ICCV.2005.27

A unifying approach to hard and probabilistic 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

121 Scopus citations

Abstract

We derive the clustering problem from first principles showing that the goal of achieving a probabilistic, or "hard", multi class clustering result is equivalent to the algebraic problem of a completely positive factorization under a doubly stochastic constraint. We show that spectral clustering, normalized cuts, kernel K-means and the various normalizations of the associated affinity matrix are particular instances and approximations of this general principle. We propose an efficient algorithm for achieving a completely positive factorization and extend the basic clustering scheme to situations where partial label information is available.

Original language	English
Title of host publication	Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005
Pages	294-301
Number of pages	8
DOIs	https://doi.org/10.1109/ICCV.2005.27
State	Published - 2005
Event	Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005 - Beijing, China Duration: 17 Oct 2005 → 20 Oct 2005

Publication series

Name	Proceedings of the IEEE International Conference on Computer Vision
Volume	I

Conference

Conference	Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005
Country/Territory	China
City	Beijing
Period	17/10/05 → 20/10/05

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10.1109/ICCV.2005.27

Cite this

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title = "A unifying approach to hard and probabilistic clustering",

abstract = "We derive the clustering problem from first principles showing that the goal of achieving a probabilistic, or {"}hard{"}, multi class clustering result is equivalent to the algebraic problem of a completely positive factorization under a doubly stochastic constraint. We show that spectral clustering, normalized cuts, kernel K-means and the various normalizations of the associated affinity matrix are particular instances and approximations of this general principle. We propose an efficient algorithm for achieving a completely positive factorization and extend the basic clustering scheme to situations where partial label information is available.",

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note = "Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005 ; Conference date: 17-10-2005 Through 20-10-2005",

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Zass, R & Shashua, A 2005, A unifying approach to hard and probabilistic clustering. in Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005., 1541270, Proceedings of the IEEE International Conference on Computer Vision, vol. I, pp. 294-301, Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005, Beijing, China, 17/10/05. https://doi.org/10.1109/ICCV.2005.27

A unifying approach to hard and probabilistic clustering. / Zass, Ron; Shashua, Amnon.
Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005. 2005. p. 294-301 1541270 (Proceedings of the IEEE International Conference on Computer Vision; Vol. I).

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

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A unifying approach to hard and probabilistic clustering

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