Skip to main content
SpringerLink
Log in

Implementation of Neural Network Learning with Minimum L 1-Norm Criteria in Fractional Order Non-gaussian Impulsive Noise Environments

  • Conference paper
Advances in Neural Networks - ISNN 2008 (ISNN 2008)

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

Included in the following conference series:

  • 3016 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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 

Download references

Author information

Authors and Affiliations

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

    Daifeng Zha

Authors
  1. Daifeng Zha
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • 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)

Publish with us

Policies and ethics

Search

Navigation