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Tensor neural network models for tensor singular value decompositions

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Abstract

Tensor decompositions have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-one outer products using either the CANDECOMP/PARAFAC, the Tucker model, or some variations thereof. The motivation of these decompositions is to find an approximate representation for a given tensor. The main propose of this paper is to develop two neural network models for finding an approximation based on t-product for a given third-order tensor. Theoretical analysis shows that each of the neural network models ensures the convergence performance. The computer simulation results further substantiate that the models can find effectively the left and right singular tensor subspace.

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Acknowledgements

We thank the editor and two anonymous reviewers for their detailed and helpful comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hexi University, Zhangye, 734000, People’s Republic of China

    Xuezhong Wang

  2. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Maolin Che

  3. School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

    Yimin Wei

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  1. Xuezhong Wang
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Correspondence to Maolin Che.

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X. Wang: This author is partially supported by Shanghai Key Laboratory of Contemporary Applied Mathematics, Natural Science Foundation of Gansu Province and Innovative Ability Promotion Project in Colleges and Universities of Gansu Province 2019B-146. M. Che: This author is supported by the National Natural Science Foundation of China under Grant 11901471. Y. Wei: This author is supported by the National Natural Science Foundation of China under Grant 11771099 and Innovation Program of Shanghai Municipal Education Commission.

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Wang, X., Che, M. & Wei, Y. Tensor neural network models for tensor singular value decompositions. Comput Optim Appl 75, 753–777 (2020). https://doi.org/10.1007/s10589-020-00167-1

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