Adaptive Linear and Normalized Combination of Radial Basis Function Networks for Function Approximation and Regression

Table 1

Description of the synthetic data sets for function approximation.

Function name	Target function expression	Distribution of independent variables	Size of samples
Zigzag	𝑔(𝑥)=sin𝑥^2−0.25𝑥	𝑥∼𝑈[0,3]	3000
Rhythm	𝑔(𝑥)=mod(𝑥,11)−58^3	𝑥∼𝑈[0,20]	1000
SinCos	𝑔(𝑥)=𝑥sin𝑥cos𝑥	𝑥∼𝑈[0,2𝜋]	2000
ExpSin	𝑔(𝑥)=2𝑥^2𝜋+exp𝑥sin(2𝜋𝑥)	𝑥∼𝑈[1,3]	4000
3-D Mexican Hat	𝑔𝑥1,𝑥2=sin𝑥^21+𝑥^22𝑥^21+𝑥^22	𝑥1∼𝑈[−5,5]; 𝑥2∼𝑈[−5,5]	2500
Gabor	𝑔𝑥1,𝑥2=𝜋2exp−2𝑥^21+𝑥^22cos2𝜋𝑥1+𝑥2	𝑥1∼𝑈[0,1]; 𝑥2∼𝑈[0,1]	2500
SwingCos	𝑔𝑥1,𝑥2=𝑥1+𝑥2+cos2𝜋𝑥1+cos2𝜋𝑥2	𝑥1∼𝑈[−1,1]; 𝑥2∼𝑈[−1,1]	2500
Exponential	𝑔𝑥1,𝑥2=𝑥1exp−𝑥^21+𝑥^22	𝑥1∼𝑈[−2,2]; 𝑥2∼𝑈[−2,2]	2500