Optimum Subspace Learning and Error Correction for Tensors

Confronted with the high-dimensional tensor-like visual data, we derive a method for the decomposition of an observed tensor into a low-dimensional structure plus unbounded but sparse irregular patterns. The optimal rank-(R1, R2, ...Rn) tensor decomposition model that we propose in this paper, could automatically explore the low-dimensional structure of the tensor data, seeking optimal dimension and basis for each mode and separating the irregular patterns. Consequently, our method accounts for the implicit multi-factor structure of tensor-like visual data in an explicit and concise manner. In addition, the optimal tensor decomposition is formulated as a convex optimization through relaxation technique. We then develop a block coordinate descent (BCD) based algorithm to efficiently solve the problem. In experiments, we show several applications of our method in computer vision and the results are promising.

• Type: Conference
• Year: 2010
• Where: ECCV
• Keywords: Computer Vision, ECCV 2010, Low-Dimensional Structure, Tensor Decomposition, Tensor-like Visual Data