Thin Plate Splines with Discontinuities and Fast Algorithms for Their Computation

Abstract

This paper discusses the problem of fitting noisy data in high dimensions. Using a reproducing kernel Hilbert space approach, the authors study thin plate splines, which preserve and incorporate discontinuities explicitly. Both smoothing and interpolating splines are computed. To cope with the formidable cost of computation, the authors propose four different fast algorithms, which are an order of magnitude faster than conventional methods. To construct the splines the authors assume that the location and type of discontinuities are known. However, this information is usually not available in practice. A discontinuity detector in high dimensions based on a residual analysis is investigated.