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Multiplicative Algorithms for Symmetric Nonnegative Tensor Factorizations and Its Applications

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Abstract

Nonnegative tensor factorization (NTF) and nonnegative Tucker decomposition (NTD) have been widely applied in high-dimensional nonnegative tensor data analysis. This paper focuses on symmetric NTF and symmetric NTD, which are the special cases of NTF and NTD, respectively. By minimizing the Euclidean distance and the generalized KL divergence, the multiplicative updating rules are proposed and the convergence under mild conditions is proved. We also show that if the solution converges based on the multiplicative updating rules, then the limit satisfies the Karush–Kuhn–Tucker optimality conditions. We illustrate the efficiency of these multiplicative updating rules via several numerical examples.

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Notes

  1. The Yale Face Database is at http://vision.ucsd.edu/content/extended-yale-face-database-b-b.

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Acknowledgements

We would like to thank the Editor-in-Chief, Prof. Chi-Wang Shu and two anonymous reviewers for very helpful comments.

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Authors and Affiliations

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

    Maolin Che

  2. School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Yimin Wei

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Correspondence to Yimin Wei.

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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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Che, M., Wei, Y. Multiplicative Algorithms for Symmetric Nonnegative Tensor Factorizations and Its Applications. J Sci Comput 83, 53 (2020). https://doi.org/10.1007/s10915-020-01233-w

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