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Mathematics 2019, 7(3), 262; https://doi.org/10.3390/math7030262

A Neural Network Approximation Based on a Parametric Sigmoidal Function

Department of Mathematics, Kunsan National University, Gunsan 54150, Korea
Received: 12 February 2019 / Revised: 5 March 2019 / Accepted: 11 March 2019 / Published: 14 March 2019
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Abstract

It is well known that feed-forward neural networks can be used for approximation to functions based on an appropriate activation function. In this paper, employing a new sigmoidal function with a parameter for an activation function, we consider a constructive feed-forward neural network approximation on a closed interval. The developed approximation method takes a simple form of a superposition of the parametric sigmoidal function. It is shown that the proposed method is very effective in approximation of discontinuous functions as well as continuous ones. For some examples, the availability of the presented method is demonstrated by comparing its numerical results with those of an existing neural network approximation method. Furthermore, the efficiency of the method in extended application to the multivariate function is also illustrated. View Full-Text
Keywords: feed-forward neural network; activation function; parametric sigmoidal function; quasi-interpolation feed-forward neural network; activation function; parametric sigmoidal function; quasi-interpolation
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Yun, B.I. A Neural Network Approximation Based on a Parametric Sigmoidal Function. Mathematics 2019, 7, 262.

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