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

Authors:
Amnon Shashua;Ron Zass;Tamir Hazan
Affiliations:
School of Engineering and Computer Science, The Hebrew University, Jerusalem;School of Engineering and Computer Science, The Hebrew University, Jerusalem;School of Engineering and Computer Science, The Hebrew University, Jerusalem
Venue:
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Year:
2006

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Abstract

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.