Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases

Rocio Gonzalez-Diaz, E. Mainar, Eduardo Paluzo-Hidalgo and B. Rubio
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Rocio Gonzalez-Diaz: Department of Applied Mathematics I, University of Sevilla, 41012 Sevilla, Spain
E. Mainar: Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50001 Zaragoza, Spain
Eduardo Paluzo-Hidalgo: Department of Applied Mathematics I, University of Sevilla, 41012 Sevilla, Spain
B. Rubio: Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50001 Zaragoza, Spain

Mathematics, 2020, vol. 8, issue 12, 1-19

Abstract: This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational bases. The approximation is achieved by finding suitable weights and control points to fit the given set of data points using a neural network and a training algorithm, called AdaMax algorithm, which is a first-order gradient-based stochastic optimization. The neural network presented in this paper is novel and based on a recent generalization of rational curves which inherit geometric properties and algorithms of the traditional rational Bézier curves. The neural network has been applied to different kinds of datasets and it has been compared with the traditional least-squares method to test its performance. The obtained results show that our method can generate a satisfactory approximation.

Keywords: normalized totally positive bases; normalized B-bases; rational bases; curve fitting; neural network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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