Orthogonality of Decision Boundaries in Complex-Valued Neural Networks

  title={Orthogonality of Decision Boundaries in Complex-Valued Neural Networks},
  author={Tohru Nitta},
  journal={Neural Computation},
This letter presents some results of an analysis on the decision boundaries of complex-valued neural networks whose weights, threshold values, input and output signals are all complex numbers. The main results may be summarized as follows. (1) A decision boundary of a single complex-valued neuron consists of two hypersurfaces that intersect orthogonally, and divides a decision region into four equal sections. The XOR problem and the detection of symmetry problem that cannot be solved with two… CONTINUE READING


Publications citing this paper.
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Publications referenced by this paper.
Showing 1-10 of 19 references

A complex numbered version of the back-propagation algorithm

  • T. Nitta
  • Proc. World Congress on Neural Networks (Vol. 3…
  • 1993
Highly Influential
8 Excerpts

Complex domain backpropagation

  • G. M. Georgiou, C. Koutsougeras
  • IEEE Trans. Circuits and Systems–II: Analog and…
  • 1992
Highly Influential
4 Excerpts

A complex back-propagation learning

  • T. Nitta, T. Furuya
  • Transactions of Information Processing Society of…
  • 1991
Highly Influential
6 Excerpts

Parallel distributed processing (Vol

  • D. E. Rumelhart, G. E. Hinton, R. J. Williams
  • 1986
Highly Influential
5 Excerpts

Neural networks in multidimensional domains

  • P. Arena, L. Fortuna, G. Muscato, M. G. Xibilia
  • Lecture Notes in Control and Information Science
  • 1998
Highly Influential
1 Excerpt

On energy function for complexvalued neural networks and its applications

  • Y. Kuroe, N. Hashimoto, T. Mori
  • In Proc. Int. Conf. on Neural Information…
  • 2002

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