Radial Basis Function Networks

Synonyms

Kernel methods; Networks with kernel functions; Neural networks; Quasi-interpolation; Radial basis function approximation; Radial basis function neural networks; Regularization networks; Support vector machines

Definition

Radial basis function networks are a means of approximation by algorithms using linear combinations of translates of a rotationally invariant function, called the radial basis function. The coefficients of these approximations usually solve a minimization problem and can also be computed by interpolation processes. Sometimes the very useful approach of quasi-interpolation is also applied where approximations are computed that do not necessarily match the target functions pointwise but satisfy certain smoothness and decay conditions. The radial basis functions constitute so-called reproducing kernels on certain Hilbert spaces or – in a slightly more general setting – semi-Hilbert spaces. In the latter case, the aforementioned approximation also contains an...