Volume 1, Issue 1, October 2016, Page: 8-12
On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions
Nikolay Kyurkchiev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Anton Iliev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria; Faculty of Mathematics and Informatics, Paisii Hilendarski University of Plovdiv, Plovdiv, Bulgaria
Received: Aug. 18, 2016;       Accepted: Oct. 12, 2016;       Published: Oct. 14, 2016
DOI: 10.11648/j.mma.20160101.12      View  3079      Downloads  80
Abstract
In this paper we study the one-sided Hausdorff distance between the Heaviside function and some transmuted activation functions. Precise upper and lower bounds for the Hausdorff distance have been obtained. Numerical examples are presented throughout the paper using the computer algebra system MATHEMATICA. The results can be successfully used in the field of applied insurance mathematics.
Keywords
Transmuted Activation Functions, Heaviside Function, Hausdorff Distance, Upper and Lower Bounds, Squashing Function
To cite this article
Nikolay Kyurkchiev, Anton Iliev, On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions, Mathematical Modelling and Applications. Vol. 1, No. 1, 2016, pp. 8-12. doi: 10.11648/j.mma.20160101.12
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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