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Top1. Introduction
Multivariable function regression is a traditional and very important problem in numerical analysis which is widely applied (Alpaydin, 2010; Bartels, Beatty, & Barsky, 1987; Bromhead & Lowe, 1988; Collatz, 1966; Park & Sandberg, 1993; Tomohiro, Sadanori, & Seiya, 2008). When no concerning on noise distribution characteristics, this problem is stated and applied through interpolation and function approximation problems. 1-D case was researched and solved by Lagrangge and Chebyshev by using polynomial as regression function. Since mid of 20th century till now, with research development and application of machine learning, image processing, computer graphic and technical problems, the regression problem has been also attracting many people to study. Among of them, selection of regression function form and good definition method is still an interested prime research topic for researchers (Blanzieri, 2003; Huan, Hien, & Huu-Tue, 2007; Schwenker, Kesler, & Gunther, 2001; Tomohiro et al., 2008).
During 3 recent decades, MLP (Multiple-Layered Perceptron), RBF (Radial Basis Function) neuron networks are effective tools to solve this problem in applications (Blanzieri, 2003; Haykin, 1999; Huan, Hien, & Huu-Tue, 2011; Looney, 1997; Rudenko & Bezsonov, 2011).
RBF regression method was proposed by Powell, introduced by Broomhead and Lowe as a neuron network (Powell, 1988; Bromhead et al., 1988). In comparison to MLP neuron network, RBF neuron network (hereinafter called RBF network) has short training period and is suitable for Regression problems. Training process of RBF network includes: 1) Defining the number of neurons in hidden layer and corresponding centre; 2) defining radius parameters of hidden neurons and the weight of output layer, in which definition of suitable neuron number in hidden layer, and the centre and radius parameters to produce a good Regression function is still an open problem (Powell, 1988; Blanzieri, 2003; Fasshauer, 2007; Pérez-Godoy, Rivera, Carmona, & del Jesus, 2014; Schwenker et al., 2001; Tomohiro et al., 2008; Weruaga & Via, 2014). The authors usually base on interpolation nodes’ distribution characteristics o determine center and radius parameter (Guang-Bin Huang, Saratchandran, & Sundararajan, 2004; Pérez-Godoy et al., 2014; Tomohiro et al., 2008; Sum, Chi-Sing Leung, & Ho, 2009).