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

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.

• Type: Conference
• Year: 2006
• Where: ECCV
• Authors: Amnon Shashua, Ron Zass, Tamir Hazan
• Keywords: Computer Vision, Conditional Independence Assumptions, Data Points, ECCV 2006, Factorization Problem, N-way Affinity Array, Super-symmetric Non-negative Factorization