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Optimum Subspace Learning and Error Correction for Tensors

  • Yin Li
  • Junchi Yan
  • Yue Zhou
  • Jie Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6313)

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,R 2,...R n ) 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.

Keywords

Irregular Pattern Matrix Completion Tensor Decomposition Optimal Rank Robust Principal Component Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yin Li
    • 1
  • Junchi Yan
    • 1
  • Yue Zhou
    • 1
  • Jie Yang
    • 1
  1. 1.Institute of Image Processing and Pattern RecogntionShanghai Jiaotong University 

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