Abstract
We present a new type of activation functions for a complex-valued neuralnetwork (CVNN). A proposed activation function is constructed such that itfixes a given ellipse. We obtain an application to a complex-valued Hopfieldneural network (CVHNN) using a special form of the introduced complexfunctions as an activation function. Considering the interesting geometricproperties of the plane curve ellipse such as focusing property, weemphasize that these properties may have possible applications in variousneural networks.
Highlights
Complex-valued neural networks (CVNN) have been used in various fields such as optoelectronics, imaging, signal processing, quantum neural devices and artificial neural information processing by many researchers
We propose a new type of complex-valued functions as an activation function for a complexvalued Hopfield neural network (CVHNN)
We propose this function as an activation function for a CVHNN
Summary
Complex-valued neural networks (CVNN) have been used in various fields such as optoelectronics, imaging, signal processing, quantum neural devices and artificial neural information processing by many researchers (see [1,2,3,4,5,6,7,8] for more details). We propose a new type of complex-valued functions as an activation function for a complexvalued Hopfield neural network (CVHNN). These functions fix a given ellipse on the complex plane. It is a well-known fact from geometry that a light ray which leaves a focus c1 of an ellipse will be reflected to other focus c2 (see [10] and [11] for more details) Using this interesting property and the following proposition, Frantz proposed an application to the open problem about trapped reflections described in [12]. We expect that our study will help to generate some new researches and applications on complex-valued neural networks
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
