SALSA – A Spatially Adaptive Local Smoothing Algorithm

We present a nonlinear integer programming formulation for fitting a spline-based regression to 2-dimensional data using an adaptive knot-selection approach, with the number and location of the knots being determined in the solution process. However, the nonlinear nature of this formulation makes its solution impractical, so we also outline a knot selection heuristic inspired by the Remes Exchange Algorithm, to produce good solutions to our formulation. This algorithm is intuitive and naturally accommodates local changes in smoothness. Results are presented for the algorithm demonstrating performance that is as good, or better, than other current methods on established benchmark functions.