Complex valued neural network with Mobius activation function

Necati Özdemir

doi:10.1016/j.cnsns.2011.03.005

Complex valued neural network with Mobius activation function

2011-12-01

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AI

N

Necati Özdemir *

B

Beyza Billur İskender

N

Nihal Yılmaz Özgür

DOI：10.1016/j.cnsns.2011.03.005

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In this work, we propose a new type of activation function for a complex valued neural network (CVNN). This activation function is a special Mobius transformation classified as reflection. It is bounded outside of the unit disk and has partial continuous derivatives but not differentiable since it does not satisfy the Cauchy-Riemann equalities. However, the fixed points set of this function is a circle. Therefore, we employ this function to a specific complex valued Hopfield neural network (CVHNN) and increase the number of fixed points of the CVHNN. Using of this activation function leads us also to guarantee the existence of fixed points of the CVHNN. It is shown that the fixed points are all asymptotically stable states of the CVHNN which indicates that the information capacity is enlarged. (C) 2011 Elsevier B.V. All rights reserved.

Keyword:

Complex valued neural networks

Mobius transformation

Reflection in a circle

Lyapunov stability

Complex valued neural network with Mobius activation function

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