Examples of Compactly Supported Functions for Radial Basis Approximations

摘要

Radial Basis Functions (RBFs) are widely used in science, engineering and finance for constructing nonlinear models of observed data. Most applications employ activation functions from a relatively small list, including Gaussians, multi-quadrics and thin plate splines. We introduce several new candidate compactly supported RBFs for approximating functions in L{sup}P (R{sup}d) via over-determined least squares. We illustrate their utility on the benchmark Mackey-Glass time series data. We observe that these new RBFs significantly reduce the number of modes required to approximate the data and produce models that have significantly improved condition numbers.