Multi-Mode Tensor Space Clustering Based on Low-Tensor-Rank Representation

Traditional subspace clustering aims to cluster data points lying in a union of vector subspaces. The vectorization of multidimensional data to perform clustering disregards much of the structure intrinsic to such data. To capture said structure, in this work we perform clustering in a high-order tensor space rather than a vector space. We develop a novel low-tensor-rank representation (LTRR) for unfolded matrices of tensor data lying in a low-rank tensor space. The representation coefficient matrix of an unfolding matrix is tensorized to a 3-order tensor, and a low-tensor-rank constraint is imposed on the resulting coefficient tensor to exploit the self-expressiveness property. Then, inspired by the multiview clustering framework, we develop a multi-mode tensor space clustering algorithm (MMTSC) that can deal with tensor space clustering with or without missing entries. The tensor is unfolded along each mode, and the coefficient matrices are obtained for each unfolded matrix. The low-tensorrank constraint is imposed on a tensor constructed from transformed coefficient tensors for each mode, thereby simultaneously capturing the low rank property of the data within each tensor space and maintaining cluster consistency across different modes. Experimental results demonstrate that the proposed MMTSC algorithm can in many cases outperform existing clustering algorithms.

Authors

• Yicong He
• George K. Atia University of Central Florida

Keywords

No keywords are indexed for this paper.