VOLTERRA MODELS AND 3-LAYER PERCEPTRONS

Citation
Vz. Marmarelis et X. Zhao, VOLTERRA MODELS AND 3-LAYER PERCEPTRONS, IEEE transactions on neural networks, 8(6), 1997, pp. 1421-1433
Citations number
41
Categorie Soggetti
Computer Application, Chemistry & Engineering","Engineering, Eletrical & Electronic","Computer Science Artificial Intelligence","Computer Science Hardware & Architecture","Computer Science Theory & Methods
ISSN journal
10459227
Volume
8
Issue
6
Year of publication
1997
Pages
1421 - 1433
Database
ISI
SICI code
1045-9227(1997)8:6<1421:VMA3P>2.0.ZU;2-2
Abstract
This paper proposes the use of a class of feedforward artificial neura l networks with polynomial activation functions (distinct for each hid den unit) for practical modeling of high-order Volterra systems, Discr ete-time Volterra models (DVM's) are often used in the study of nonlin ear physical and physiological systems using stimulus-response data, H owever, their practical use has been hindered by computational limitat ions that confine them to low-order nonlinearities (i.e., only estimat ion of low-order kernels is practically feasible), Since three-layer p erceptrons (TLP's) can be used to represent input-output nonlinear map pings of arbitrary order, this paper explores the basic relations betw een DVM and TLP with tapped-delay inputs in the context of nonlinear s ystem modeling, A variant of TLP with polynomial activation functions- termed ''separable Volterra networks'' (SVN's)-is found particularly u seful in deriving explicit relations with DVM and in obtaining practic able models of highly nonlinear systems from stimulus-response data, T he conditions under which the two approaches yield equivalent represen tations of the input-output relation are explored, and the feasibility of DVM estimation via equivalent SVN training using backpropagation i s demonstrated by computer-simulated examples and compared with result s from the Laguerre expansion technique (LET), The use of SVN models a llows practicable modeling of high-order nonlinear systems, thus remov ing the main practical limitation of the DVM approach.