Multiquadric radial basis functions for representing multidimensional high energy physics data

Abstract

We examine how basis functions can be used to represent multidimensional data and argue that radial basis functions are a natural choice. Of all the possible radial basis functions, multiquadrics, counter-intuitively, turn out to be supremely suitable for representing high energy physics event densities, and probably many other forms of scientific data, because they fulfill the physicists' requirements of sensible non-erratic behaviour and follow significant variations in a smooth and faithful way. The stochastic nature of high energy physics data often gives rise to unwelcome statistical fluctuations; our algorithm can be used to smooth these out. The smoothed function is much easier to visualise than the original scattered events. A suite of Fortran subroutines has been written in the framework of current high energy physics data analysis systems, HBOOK and PAW.