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Matrix-Valued Hopfield Neural Networks

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Advances in Neural Networks – ISNN 2016 (ISNN 2016)

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Abstract

In this paper, we introduce matrix-valued Hopfield neural networks, for which the states, outputs, weights and thresholds are all square matrices. Matrix-valued neural networks represent a generalization of the complex-, hyperbolic-, quaternion- and Clifford-valued neural networks that have been intensively studied over the last few years. The dynamics of these networks is studied by giving an expression for the energy function, and proving that it is indeed an energy function for the proposed network.

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Author information

Authors and Affiliations

  1. Department of Computer and Software Engineering, Polytechnic University Timişoara, Blvd. V. Pârvan, No. 2, 300223, Timişoara, Romania

    Călin-Adrian Popa

Authors
  1. Călin-Adrian Popa
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Correspondence to Călin-Adrian Popa .

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Editors and Affiliations

  1. The Chinese Academy of Sciences, Beijing, China

    Long Cheng

  2. Huazhong University of Science and Tech., Wuhan, Jiangsu, China

    Qingshan Liu

  3. Russian Academy of Sciences, SPIIRAS, St. Petersburg, Russia

    Andrey Ronzhin

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Popa, CA. (2016). Matrix-Valued Hopfield Neural Networks. In: Cheng, L., Liu, Q., Ronzhin, A. (eds) Advances in Neural Networks – ISNN 2016. ISNN 2016. Lecture Notes in Computer Science(), vol 9719. Springer, Cham. https://doi.org/10.1007/978-3-319-40663-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-40663-3_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40662-6

  • Online ISBN: 978-3-319-40663-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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