title: Comparing fixed and variable-width Gaussian networks.
abstract: The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described.
authors.affiliation: Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07 Prague, Czech Republic. Electronic address: vera@cs.cas.cz.
authors.forename: Věra
authors.initials: V
authors.lastname: Kůrková
authors.affiliation: Department of Mathematics and Statistics, Georgetown University, 3700 Reservoir Rd., N.W., Washington, DC 20057, USA. Electronic address: kainen@georgetown.edu.
authors.forename: Paul C
authors.initials: PC
authors.lastname: Kainen
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016571:Neural Networks, Computer; D016011:Normal Distribution
keywords: Argminima of error functionals; Functionally equivalent networks; Gaussian radial and kernel networks; Stabilizers defined by Gaussian kernels; Universal approximators