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Quaternion-Valued Feedforward Neural Network Based Time Series Forecast

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Communications, Signal Processing, and Systems (CSPS 2017)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 463))

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Abstract

Currently, the quaternion-valued feedforward neural network (QFNN) has been proposed for image compression and has a more superior performance than the real-valued feedforward neural network (FNN). However, the used quaternion activation function is a split quaternion function, thus it may not preserve the cross-information within the components of the data and for time series forecast, the established model is a strictly linear model which may not be appropriate for noncircular quaternion-valued signal processing.

In this paper, a fully quaternion activation function is employed to design the QFNN and an augmented QFNN (AQFNN) is proposed. They are derived by using recent studies in the augmented quaternion statistics and the HR-calculus. With the augmented quaternion statistics, the AQFNN can process quaternion-valued noncircular signals, effectively. Simulations on both benchmark circular and noncircular quaternion-valued signals, and real-world quaternion-valued signals support the analysis.

Research supported by NSFC under Grant No. 61571159 and No. 61571157.

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Authors and Affiliations

  1. Harbin Institute of Technology, Weihai, China

    Xiaodong Li, Changjun Yu, Fulin Su, Aijun Liu & Xuguang Yang

Authors
  1. Xiaodong Li
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  2. Changjun Yu
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  3. Fulin Su
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  4. Aijun Liu
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  5. Xuguang Yang
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Corresponding author

Correspondence to Changjun Yu .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Texas at Arlington, Arlington, Texas, USA

    Qilian Liang

  2. College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin, China

    Jiasong Mu

  3. Harbin Institute of Technology, Harbin, Heilongjiang, China

    Min Jia

  4. College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin, China

    Wei Wang

  5. College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin, China

    Xuhong Feng

  6. College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin, China

    Baoju Zhang

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Li, X., Yu, C., Su, F., Liu, A., Yang, X. (2019). Quaternion-Valued Feedforward Neural Network Based Time Series Forecast. In: Liang, Q., Mu, J., Jia, M., Wang, W., Feng, X., Zhang, B. (eds) Communications, Signal Processing, and Systems. CSPS 2017. Lecture Notes in Electrical Engineering, vol 463. Springer, Singapore. https://doi.org/10.1007/978-981-10-6571-2_196

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  • DOI: https://doi.org/10.1007/978-981-10-6571-2_196

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6570-5

  • Online ISBN: 978-981-10-6571-2

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