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Link to original content: https://unpaywall.org/10.1007/978-3-540-87732-5_32
Implementation of Neural Network Learning with Minimum L 1-Norm Criteria in Fractional Order Non-gaussian Impulsive Noise Environments | SpringerLink
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Implementation of Neural Network Learning with Minimum L 1-Norm Criteria in Fractional Order Non-gaussian Impulsive Noise Environments

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Advances in Neural Networks - ISNN 2008 (ISNN 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5263))

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Abstract

Minimum L 1-norm optimization model has found extensive applications in linear parameter estimations. L 1-norm model is robust in non Gaussian alpha stable distribution error or noise environments, especially for signals that contain sharp transitions (such as biomedical signals with spiky series) or dynamic processes. However, its implementation is more difficult due to discontinuous derivatives, especially compared with the least-squares (L 2-norm) model. In this paper, a new neural network for solving L 1-norm optimization problems is presented. It has been proved that this neural network is able to converge to the exact solution to a given problem. Implementation of L 1-norm optimization model is presented, where a new neural network is constructed and its performance is evaluated theoretically and experimentally.

This work is supported by National Science Foundation of China under Grant 60772037.

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References

  1. Cichocki, A., Unbehauen, R.: Neural Networks for Solving Systems of Linear Equation–Part II: Minimax and Least Absolute Value Problems. IEEE Trans. Circuits Syst. II 39, 619–633 (1992)

    Article  MATH  Google Scholar 

  2. Nikias, C.L., Shao, M.: Signal Processing with Alpha-Stable Distribution and Applications, 1st edn. Wiley, Chichester (1995)

    Google Scholar 

  3. Georgiou, P.G., Tsakalides, P., Kyriakakis, C.: Alpha-Stable Modeling of Noise and Robust Time-Delay Estimation in the Presence of Impulsive Noise. IEEE Trans. on Multimedia 1, 291–301 (1999)

    Article  Google Scholar 

  4. Bloomfield, P., Steiger, W.L.: Least Absolute Deviations: Theory Applications and Algorithms. Brikhäuser, Boston (1983)

    MATH  Google Scholar 

  5. Xia, Y.S.: A New Neural Network for Solving Linear Programming Problems and Its Application. IEEE Trans. Neural Networks. 7, 525–529 (1996)

    Article  Google Scholar 

  6. Xia, Y.S., Wang, J.: A General Methodology for Designing Globally Convergent Optimization Neural Networks. IEEE Trans. Neural Networks 9, 1331–1343 (1998)

    Article  Google Scholar 

  7. Luenberger, D.G.: Introduction to Linear and Nonlinear Programming. Addison- Wesley, New York (1973)

    MATH  Google Scholar 

  8. Zala, C.A., Barrodale, I., Kennedy, J.S.: High-resolution Signal and Noise Field Estimation Using the L1 (least absolute values) Norm. IEEE J. Oceanic Eng. OE- 12, 253–264 (1987)

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Electronic Engineering, Jiujiang University, 332005, Jiujiang, China

    Daifeng Zha

Authors
  1. Daifeng Zha
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghu University, 100084, Beijing, China

    Fuchun Sun

  2. Institute TAMS (Technical Aspects of Multimodal Systems), department of Informatics, University of Hamburg, Vogt-Koelln-Straße 30, 22527, Hamburg, Germany

    Jianwei Zhang

  3. Intel China Research Center, 8/F, Peking University, Department of Machine Intelligence, 100871, Beijing, China

    Ying Tan

  4. Department of Mathematics, Southeast University, 210096, Nanjing, China

    Jinde Cao

  5. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

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© 2008 Springer-Verlag Berlin Heidelberg

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Zha, D. (2008). Implementation of Neural Network Learning with Minimum L 1-Norm Criteria in Fractional Order Non-gaussian Impulsive Noise Environments. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87732-5_32

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  • DOI: https://doi.org/10.1007/978-3-540-87732-5_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87731-8

  • Online ISBN: 978-3-540-87732-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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