Multi-way clustering using super-symmetric non-negative tensor factorization

Amnon Shashua*, Ron Zass, Tamir Hazan

*Corresponding author for this work

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

76 Scopus citations


We consider the problem of clustering data into k ≥ 2 clusters given complex relations - going beyond pairwise - between the data points. The complex n-wise relations are modeled by an n-way array where each entry corresponds to an affinity measure over an n-tuple of data points. We show that a probabilistic assignment of data points to clusters is equivalent, under mild conditional independence assumptions, to a super-symmetric non-negative factorization of the closest hyper-stochastic version of the input n-way affinity array. We derive an algorithm for finding a local minimum solution to the factorization problem whose computational complexity is proportional to the number of n-tuple samples drawn from the data. We apply the algorithm to a number of visual interpretation problems including 3D multi-body segmentation and illumination-based clustering of human faces.

Original languageAmerican English
Title of host publicationComputer Vision - ECCV 2006, 9th European Conference on Computer Vision, Proceedings
Number of pages14
StatePublished - 2006
Event9th European Conference on Computer Vision, ECCV 2006 - Graz, Austria
Duration: 7 May 200613 May 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3954 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th European Conference on Computer Vision, ECCV 2006


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