Approximation Using Cubic B-Splines with Improved Training Speed and Accuracy

Abstract

When using cubic B-splines, the quality of approximation depends on the placement of the knots. This paper describes the practical application of a new method for the selection of knot densities. Using a filtering and merging algorithm to split the input space into distinct regions, the number of equidistant knots in each subdivision of the space can be calculated in order to keep the approximation error below a predefined limit. In addition to the smoothing of the error surface, the technique also has the advantage of reducing the computational cost of calculating the spline approximation parameters.