Artículo
Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases
Autor/es | González Díaz, Rocío
Mainardes, Emerson Paluzo Hidalgo, Eduardo Rubio Serrano, Beatriz |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I |
Fecha de publicación | 2020-12-10 |
Fecha de depósito | 2021-02-03 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) European Union (UE) |
Identificador del proyecto | PID2019-107339GB-100
PGC2018-096321-B-I00 E41_17R |
Cita | González Díaz, R., Mainardes, E., Paluzo Hidalgo, E. y Rubio Serrano, B. (2020). Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases. Mathematics, 8 (12), 2197-1-2197-19. |
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