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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Multi-way Clustering Using Super-Symmetric Non-negative Tensor Factorization
verfasst von : Amnon Shashua, Ron Zass, Tamir Hazan
Erschienen in: Computer Vision – ECCV 2006
Verlag: Springer Berlin Heidelberg
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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.