Optimum subspace learning and error correction for tensors

Abstract

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-(R 1,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. © 2010 Springer-Verlag.