TY - JOUR

T1 - Automatic curve fitting based on radial basis functions and a hierarchical genetic algorithm

AU - Trejo-Caballero, G.

AU - Rostro-Gonzalez, H.

AU - Garcia-Capulin, C. H.

AU - Ibarra-Manzano, O. G.

AU - Avina-Cervantes, J. G.

AU - Torres-Huitzil, C.

N1 - Publisher Copyright:
© 2015 G. Trejo-Caballero et al.

PY - 2015

Y1 - 2015

N2 - Curve fitting is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of data points, possibly noisy, the goal is to build a compact representation of the curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Despite the large number of methods available to tackle this problem, it remains challenging and elusive. In this paper, a new method to tackle such problem using strictly a linear combination of radial basis functions (RBFs) is proposed. To be more specific, we divide the parameter search space into linear and nonlinear parameter subspaces. We use a hierarchical genetic algorithm (HGA) to minimize a model selection criterion, which allows us to automatically and simultaneously determine the nonlinear parameters and then, by the least-squares method through Singular Value Decomposition method, to compute the linear parameters. The method is fully automatic and does not require subjective parameters, for example, smooth factor or centre locations, to perform the solution. In order to validate the efficacy of our approach, we perform an experimental study with several tests on benchmarks smooth functions. A comparative analysis with two successful methods based on RBF networks has been included.

AB - Curve fitting is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of data points, possibly noisy, the goal is to build a compact representation of the curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Despite the large number of methods available to tackle this problem, it remains challenging and elusive. In this paper, a new method to tackle such problem using strictly a linear combination of radial basis functions (RBFs) is proposed. To be more specific, we divide the parameter search space into linear and nonlinear parameter subspaces. We use a hierarchical genetic algorithm (HGA) to minimize a model selection criterion, which allows us to automatically and simultaneously determine the nonlinear parameters and then, by the least-squares method through Singular Value Decomposition method, to compute the linear parameters. The method is fully automatic and does not require subjective parameters, for example, smooth factor or centre locations, to perform the solution. In order to validate the efficacy of our approach, we perform an experimental study with several tests on benchmarks smooth functions. A comparative analysis with two successful methods based on RBF networks has been included.

UR - http://www.scopus.com/inward/record.url?scp=84956906034&partnerID=8YFLogxK

U2 - 10.1155/2015/731207

DO - 10.1155/2015/731207

M3 - Article

AN - SCOPUS:84956906034

SN - 1024-123X

VL - 2015

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

M1 - 731207

ER -