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.
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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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Li, Y., Yan, J., Zhou, Y., Yang, J. (2010). Optimum Subspace Learning and Error Correction for Tensors. In: Daniilidis, K., Maragos, P., Paragios, N. (eds) Computer Vision – ECCV 2010. ECCV 2010. Lecture Notes in Computer Science, vol 6313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15558-1_57
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DOI: https://doi.org/10.1007/978-3-642-15558-1_57
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