A  Derived Heterogeneous Transfer Function from Convolution of Symmetric Hardlimit and Hyperbolic Tangent Sigmoid Transfer Functions

Christopher Godwin  Udomboso; Olamide Olufunmilayo  Ilori

doi:10.4314/just.v40i1.1260

Christopher Godwin Udomboso (PhD) Department of Statistics, University of Ibadan
Ms Olamide Olufunmilayo Ilori University of Ibadan

DOI: https://doi.org/10.4314/just.v40i1.1260

Keywords: variance, mean, probability distribution, convolution, Transfer function

Abstract

This study derived a new heterogeneous transfer function of the Statistical Neural Network from a convolution of two transfer functions: the Symmetric Hard Limit and Hyperbolic Tangent Sigmoid, showing their various mathematical forms. The properties of the derived function were examined. Results show that it is a proper probability distribution with distributional properties shown to exist with mean 0, and variance . Numerical illustrations showed that the derived heterogeneous model is more efficient than its homogeneous forms, as indicated from their respective predictive performances. From the foregoing, the use of homogeneous models of the statistical neural networks in solving empirical problems is encouraged, for effective outcomes.

Author Biographies

Christopher Godwin Udomboso (PhD), Department of Statistics, University of Ibadan

Dr Christopher Godwin UDOMBOSO

Dr Christopher Godwin Udomboso is a faculty member in the Department of Statistics, University of Ibadan, Nigeria, with interest in Machine/Statistical Learning. His major research has been on neural networks, with applications to natural and physical sciences. He was a Postdoctoral Fellow at the North-West University, South Africa (2015-2016). He is Senior Associate Fellow with the Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy. He is an external examiner to the Department of Statistics, North-West University, Mafikeng Campus, South Africa, as well as a few other local universities. He is a member of some local and international professional group.

Ms Olamide Olufunmilayo Ilori, University of Ibadan

Ms Olamide Olufunmilayo Ilori holds a B.Sc. (Statistics) from the University of Abuja, and M.Sc. (Statistics) from the University of Ibadan, both in Nigeria. She works in the field of Machine/Statistical Learning. Her M.Sc. dissertation was one of the outstanding work in machine learning applied to a challenging problem in the petroleum sector, coming from a third world university. She is already thinking of expanding the work in her doctoral program.