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2017 IEEE International Conference on Computer Vision (ICCV) (2017)
Venice, Italy
Oct. 22, 2017 to Oct. 29, 2017
ISSN: 2380-7504
ISBN: 978-1-5386-1032-9
pp: 5698-5706
ABSTRACT
Using the matrix product state (MPS) representation of the recently proposed tensor ring (TR) decompositions, in this paper we propose a TR completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. We propose a novel initialization method and analyze the computational complexity of the TR completion algorithm. The numerical comparison between the TR completion algorithm and the existing algorithms that employ a low rank tensor train (TT) approximation for data completion shows that our method outperforms the existing ones for a variety of real computer vision settings, and thus demonstrates the improved expressive power of tensor ring as compared to tensor train.
INDEX TERMS
computer vision, tensors
CITATION

W. Wang, V. Aggarwal and S. Aeron, "Efficient Low Rank Tensor Ring Completion," 2017 IEEE International Conference on Computer Vision (ICCV), Venice, Italy, 2018, pp. 5698-5706.
doi:10.1109/ICCV.2017.607
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