Comparing Fixed and Variable-Width Gaussian Networks

0428366 - ÚI 2015 RIV GB eng J - Journal Article
Kůrková, Věra - Kainen, P.C.
Comparing Fixed and Variable-Width Gaussian Networks.
Neural Networks. Roč. 57, September (2014), s. 23-28. ISSN 0893-6080. E-ISSN 1879-2782
R&D Projects: GA MŠMT(CZ) LD13002
Institutional support: RVO:67985807
Keywords : Gaussian radial and kernel networks * Functionally equivalent networks * Universal approximators * Stabilizers defined by Gaussian kernels * Argminima of error functionals
Subject RIV: IN - Informatics, Computer Science
Impact factor: 2.708, year: 2014

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 (RKHSs)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.
Permanent Link: http://hdl.handle.net/11104/0233708