Choosing the best value of shape parameter in radial basis functions by Leave-P-Out Cross Validation

The radial basis functions (RBFs) meshless method has high accuracy for the interpolation of scattered data in high dimensions. Most of the RBFs depend on a parameter, called shape parameter which plays a significant role to specify the accuracy of the RBF method. In this paper, we present three algorithms to choose the optimal value of the shape parameter. These are based on Rippa’s theory to remove data points from the data set and results obtained by Fasshauer and Zhang for the iterative approximate moving least square (AMLS) method. Numerical experiments confirm stable solutions with high accuracy compared to other methods.

Keywords:

Radial basis functions , Shape Parameter , Leave-One-Out Cross Validation , Leave-Two-Out Cross Validation , Approximate Moving Least Squares