Chapter 4. Complex Nonlinear Activation Functions

  1. Danilo P. Mandic1,
  2. Vanessa Su Lee Goh2

Published Online: 16 APR 2009

DOI: 10.1002/9780470742624.ch4

Book Title

Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models

Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models

Additional Information

How to Cite

Mandic, D. P. and Goh, V. S. L. (2009) Complex Nonlinear Activation Functions, in Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470742624.ch4

Author Information

  1. 1

    Imperial College London, UK

  2. 2

    Shell EP, Europe, UK

Publication History

  1. Published Online: 16 APR 2009
  2. Published Print: 17 APR 2009

ISBN Information

Print ISBN: 9780470066355

Online ISBN: 9780470742624

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CHAPTER TOOLS

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Keywords:

  • complex nonlinear activation functions;
  • Taylor series representation;
  • Laurent series representation;
  • singularities of complex functions;
  • universal function approximation;
  • nonlinear activation functions for complex neural networks;
  • split-complex approach;
  • real–imaginary split-complex approach;
  • Möbius transformation framework for analysis of mappings

Summary

This chapter contains sections titled:

  • Properties of Complex Functions

  • Universal Function Approximation

  • Nonlinear Activation Functions for Complex Neural Networks

  • Generalised Splitting Activation Functions (GSAF)

  • Summary: Choice of the Complex Activation Function

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