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A Unified Self-Stabilizing Neural Network Algorithm for Principal Takagi Component Extraction

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Abstract

In this paper, we develop efficient methods for the computation of the Takagi components and the Takagi subspaces of complex symmetric matrices via the complex-valued neural network models. Firstly, we present a unified self-stabilizing neural network learning algorithm for principal Takagi components and study the stability of the proposed unified algorithms via the fixed-point analysis method. Secondly, the unified algorithm for extracting principal Takagi components is generalized to compute the principal Takagi subspace. Thirdly, we prove that the associated differential equations will globally asymptotically converge to an invariance set and the corresponding energy function attains a unique global minimum if and only if its state matrices span the principal Takagi subspace. Finally, numerical simulations are carried out to illustrate the theoretical results.

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Acknowledgements

The authors would like to thank the Editor and two anonymous reviewers for their careful and detailed comments on our paper.

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

    Xuezhong Wang

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

    Yimin Wei

Authors
  1. Maolin Che
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  2. Xuezhong Wang
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  3. Yimin Wei
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Correspondence to Yimin Wei.

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Maolin Che: This author is supported by the National Natural Science Foundation of China under grant 11901471. Xuezhong Wang: Partial work is finished when the author visited Shanghai Key Laboratory of Contemporary Applied Mathematics in 2019 and supported by the National Natural Science Foundation of China under Grant 11771099. Yimin Wei: This author is supported by Innovation Program of Shanghai Municipal Education Commission.

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Che, M., Wang, X. & Wei, Y. A Unified Self-Stabilizing Neural Network Algorithm for Principal Takagi Component Extraction. Neural Process Lett 51, 591–610 (2020). https://doi.org/10.1007/s11063-019-10109-6

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