Optimum subspace learning and error correction for tensors

Authors:
Yin Li;Junchi Yan;Yue Zhou;Jie Yang
Affiliations:
Institute of Image Processing and Pattern Recogntion, Shanghai Jiaotong University;Institute of Image Processing and Pattern Recogntion, Shanghai Jiaotong University;Institute of Image Processing and Pattern Recogntion, Shanghai Jiaotong University;Institute of Image Processing and Pattern Recogntion, Shanghai Jiaotong University
Venue:
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Year:
2010

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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-(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.