Automatic knot adjustment for b-spline smoothing approximation using improved clustering algorithm

Smoothing b-splines constitute a powerful and popular methodology for performing nonparametric regression with high accuracy. It is well known that the placement of the knots in spline smoothing approximation has an important and considerable effect on the behavior of the final approximation. For this purpose, in this paper a novel methodology is presented for optimal placement and selections of knots, in order to approximate or fit curves to data, using smoothing splines. A new method based on improved clustering algorithm is used to optimally select a reduced number of knots for constructing the base of the b-spline, while ensuring the best accuracy.