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Multi-way Clustering Using Super-Symmetric Non-negative Tensor Factorization

  • Amnon Shashua
  • Ron Zass
  • Tamir Hazan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3954)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Amnon Shashua
    • 1
  • Ron Zass
    • 1
  • Tamir Hazan
    • 1
  1. 1.School of Engineering and Computer ScienceThe Hebrew UniversityJerusalemIsrael

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