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A Mixture of Nuclear Norm and Matrix Factorization for Tensor Completion

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Abstract

In this paper, we propose a mixture model for tensor completion by combining the nuclear norm with the low-rank matrix factorization. To solve this model, we develop two algorithms: non-smooth low-rank tensor completion (NS-LRTC), smooth low-rank tensor completion (S-LRTC). When the sampling rate (SR) is high, our experiments on real-world data show that the NS-LRTC algorithm outperforms other tested methods in running time and recovery quality. In addition, whatever the SR is, the proposed S-LRTC algorithm delivers state-of-art recovery performance compared with other tested approaches. Although the objective function in our model is non-convex and non-differentiable, we prove that every cluster point of the sequence generated by NS-LRTC or S-LRTC is a stationary point.

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Notes

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  3. http://trace.eas.asu.edu/yuv/.

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Acknowledgements

We thank the anonymous referees for their detailed comment, which helped to improve the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, People’s Republic of China

    Shangqi Gao & Qibin Fan

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  1. Shangqi Gao
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  2. Qibin Fan
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Correspondence to Qibin Fan.

Additional information

This research was supported by the National Science Foundation of China under Grant 61179039 and the National Key Basic Research Development Program (973 Program) of China under Grant 2011CB707100.

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Gao, S., Fan, Q. A Mixture of Nuclear Norm and Matrix Factorization for Tensor Completion. J Sci Comput 75, 43–64 (2018). https://doi.org/10.1007/s10915-017-0521-9

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  • DOI: https://doi.org/10.1007/s10915-017-0521-9

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