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

Author

Listed:
  • Rocio Gonzalez-Diaz

    (Department of Applied Mathematics I, University of Sevilla, 41012 Sevilla, Spain
    The authors contributed equally to this work.
    The authors are partially supported by MICINN, FEDER/UE under grant PID2019-107339GB-100.)

  • E. Mainar

    (Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50001 Zaragoza, Spain
    The authors contributed equally to this work.
    The authors are partially supported through the Spanish research grant PGC2018-096321-B-I00 (MCIU/AEI), by Gobierno de Aragón (E41_17R ) and by Feder 2014-2020 “Construyendo Europa desde Aragón”.)

  • Eduardo Paluzo-Hidalgo

    (Department of Applied Mathematics I, University of Sevilla, 41012 Sevilla, Spain
    The authors contributed equally to this work.
    The authors are partially supported by MICINN, FEDER/UE under grant PID2019-107339GB-100.)

  • B. Rubio

    (Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50001 Zaragoza, Spain
    The authors contributed equally to this work.
    The authors are partially supported through the Spanish research grant PGC2018-096321-B-I00 (MCIU/AEI), by Gobierno de Aragón (E41_17R ) and by Feder 2014-2020 “Construyendo Europa desde Aragón”.)

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.

Suggested Citation

  • Rocio Gonzalez-Diaz & E. Mainar & Eduardo Paluzo-Hidalgo & B. Rubio, 2020. "Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases," Mathematics, MDPI, vol. 8(12), pages 1-19, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2197-:d:459600
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