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Low tensor-ring rank completion: parallel matrix factorization with smoothness on latent space

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Abstract

In recent years, tensor ring (TR) decomposition has drawn a lot of attention and was successfully applied to tensor completion problem, due to its more compact representation ability. As well known, both global and local structural information is important for tensor completion problem. Although the existing TR-based completion algorithms obtain the impressive performance in visual-data inpainting by using low-rank global structure information, most of them didn’t take into account local smooth property which is often exhibited in visual data. To further improve visual-data inpainting performance, both low-rank and piecewise smooth structures are incorporated in our model. Instead of directly applying local smooth constraint on the data surface, we impose the smoothness on its latent TR-space, which greatly reduces computational cost especially for large-scale data. Extensive experiments on real-world visual data show that our model not only obtains the state-of-the-art performance, but also is rather stable to the TR-ranks owing to the local smooth constraint.

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The data that support the finding of this study are available from the corresponding author or first author upon reasonable request.

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Acknowledgements

This work has been supported in part by the National Natural Science Foundation of China (No. 62203128, 52171331), in part by the Guangdong Province Key Field R &D Program, China (No. 2020B0101050001), and in part by the Science and Technology Planning Project of Guangzhou City under Grants 202102010411.

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  1. **shi Yu and Guoxu Zhou contributed equally to this work.

Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, 510006, China

    **shi Yu & Tao Zou

  2. School of Automation, Guangdong University of Technology, Guangzhou, 510006, China

    Guoxu Zhou

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  1. **shi Yu
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  2. Tao Zou
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  3. Guoxu Zhou
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Correspondence to Tao Zou.

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Yu, J., Zou, T. & Zhou, G. Low tensor-ring rank completion: parallel matrix factorization with smoothness on latent space. Neural Comput & Applic 35, 7003–7016 (2023). https://doi.org/10.1007/s00521-022-08023-5

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