Automatically assigned DDC number: 00632
Manually assigned DDC number: 00632

Number of references: 8

Title: Recent Results and Mathematical Methods for Functional Approximation by Neural Networks

Author:

Subject: Paul C. Kainen Recent Results and Mathematical Methods for Functional Approximation by Neural Networks

Description: We describe various models for functional approximation by neural networks, including recent "dimensionindependent " results and emphasizing geometry and topology. These are compared with the more general theory of parametric approximation. Some ideas for heuristic improvement of neural networks are given and the issues of uniqueness and continuity of parameter selection are discussed. Keywords. Feedforward architectures, parallel computation, best approximants, geometric models. 1 Introduction The general setting of parameterized approximation by neural networks is that given a target function f : R d ! R m and a desired accuracy " ? 0, one attempts to find a parameter vector fi such that kf0Afik ! "; where Afi denotes the input-output function produced by a neural network architecture A using as "weights" fi. When the input dimension is d and the output dimension is 1, Afi : R d ! R. For example, if A is the standard perceptron architecture with activation function /, k hi...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1997-05-18

Format: ps

Identifier: http://citeseer.ist.psu.edu/174869.html

Source: http://www.clark.net/pub/kainen/survey.ps

Language: en

Relation:

Relation:

Relation:

Relation:

Relation:

Relation:

Relation:

Relation:

Rights: unrestricted

Graph

<?xml version="1.0" encoding="UTF-8"?>

<references_metadata>

<rec ID="/273383.html" Type="inproceedings" CiteSeer_Book="Advances in Neural Information Processing Systems" CiteSeer_Volume="" Title="A Framework for the Cooperation of Learning Algorithms,">

<identifier Org="ISBN:0262201070" Paper_ID="/273383.html" Extracted="0262201070" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:0444894888" Paper_ID="/273383.html" Extracted="0444894888" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:0780309111" Paper_ID="/273383.html" Extracted="0780309111" DDC="620.82" Normalized_DDC="62082" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:0780311043" Paper_ID="/273383.html" Extracted="0780311043" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:0780314212" Paper_ID="/273383.html" Extracted="0780314212" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:0780332113" Paper_ID="/273383.html" Extracted="0780332113" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:0780360109" Paper_ID="/273383.html" Extracted="0780360109" DDC="621.382/2" Normalized_DDC="6213822" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:0818679190" Paper_ID="/273383.html" Extracted="0818679190" />

<identifier Org="ISBN:0819408751" Paper_ID="/273383.html" Extracted="0819408751" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:3211826920" Paper_ID="/273383.html" Extracted="3211826920" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:3540643419" Paper_ID="/273383.html" Extracted="3540643419" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:3540644105" Paper_ID="/273383.html" Extracted="3540644105" DDC="006.3/7" Normalized_DDC="00637" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:3540663665" Paper_ID="/273383.html" Extracted="3540663665" DDC="006.4/2" Normalized_DDC="00642" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:3790815136" Paper_ID="/273383.html" Extracted="3790815136" DDC="629.8/92" Normalized_DDC="629892" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:8173713936" Paper_ID="/273383.html" Extracted="8173713936" />

<identifier Org="ISBN:9051991002" Paper_ID="/273383.html" Extracted="9051991002" DDC="004/.35" Normalized_DDC="00435" Normalized_Weight="0.06666666666666667" />

<identifier Org="ISBN:981023175X" Paper_ID="/273383.html" Extracted="981023175X" DDC="602/.85/632" Normalized_DDC="60285632" Normalized_Weight="0.06666666666666667" />

</rec>

<rec ID="/364490.html" Type="article" CiteSeer_Book="IEEE Transactions on Neural Networks" CiteSeer_Volume="6" Title="Approximation Capability to Functions of Several Variables Nonlinear Functionals and Operators by Radial Basis Function Neural Networks,">

<identifier Org="ISBN:0340741643" Paper_ID="/364490.html" Extracted="0340741643" DDC="006.4" Normalized_DDC="0064" Normalized_Weight="0.1" />

<identifier Org="ISBN:0471139467" Paper_ID="/364490.html" Extracted="0471139467" DDC="621.3/03" Normalized_DDC="621303" Normalized_Weight="0.1" />

<identifier Org="ISBN:0780314220" Paper_ID="/364490.html" Extracted="0780314220" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.1" />

<identifier Org="ISBN:0780335511" Paper_ID="/364490.html" Extracted="0780335511" />

<identifier Org="ISBN:0780336763" Paper_ID="/364490.html" Extracted="0780336763" DDC="621.382/2" Normalized_DDC="6213822" Normalized_Weight="0.1" />

<identifier Org="ISBN:0780364929" Paper_ID="/364490.html" Extracted="0780364929" />

<identifier Org="ISBN:0792382900" Paper_ID="/364490.html" Extracted="0792382900" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.1" />

<identifier Org="ISBN:1568812175" Paper_ID="/364490.html" Extracted="1568812175" DDC="616.07/54" Normalized_DDC="6160754" Normalized_Weight="0.1" />

<identifier Org="ISBN:1599048973" Paper_ID="/364490.html" Extracted="1599048973" DDC="332.0285/632" Normalized_DDC="3320285632" Normalized_Weight="0.1" />

<identifier Org="ISBN:3540211535" Paper_ID="/364490.html" Extracted="3540211535" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.1" />

<identifier Org="ISBN:354026972X" Paper_ID="/364490.html" Extracted="354026972X" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.1" />

<identifier Org="ISBN:3540341692" Paper_ID="/364490.html" Extracted="3540341692" />

<identifier Org="ISBN:3540743766" Paper_ID="/364490.html" Extracted="3540743766" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.1" />

</rec>

<rec ID="/612476.html" Type="misc" CiteSeer_Book="" CiteSeer_Volume="" Title="Network Approximation of Dynamical Systems,">

<identifier Org="ISBN:0471349119" Paper_ID="/612476.html" Extracted="0471349119" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.5" />

<identifier Org="ISBN:0780330749" Paper_ID="/612476.html" Extracted="0780330749" />

<identifier Org="ISBN:0780366859" Paper_ID="/612476.html" Extracted="0780366859" />

<identifier Org="ISBN:0817639608" Paper_ID="/612476.html" Extracted="0817639608" DDC="621.382/2/028563" Normalized_DDC="6213822028563" Normalized_Weight="0.5" />

</rec>

<rec ID="/17249.html" Type="misc" CiteSeer_Book="" CiteSeer_Volume="" Title="A general feedforward neural network model,">

<identifier Org="ISBN:0387284850" Paper_ID="/17249.html" Extracted="0387284850" DDC="006.32" Normalized_DDC="00632" Normalized_Weight="1.0" />

</rec>

<rec ID="/124464.html" Type="misc" CiteSeer_Book="" CiteSeer_Volume="" Title="Approximation error bounds that use VC-bounds,">

<identifier Org="ISBN:0817639896" Paper_ID="/124464.html" Extracted="0817639896" DDC="629.8/9" Normalized_DDC="62989" Normalized_Weight="0.25" />

<identifier Org="ISBN:1586033417" Paper_ID="/124464.html" Extracted="1586033417" DDC="006.3/1" Normalized_DDC="00631" Normalized_Weight="0.25" />

<identifier Org="ISBN:1852335394" Paper_ID="/124464.html" Extracted="1852335394" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.25" />

<identifier Org="ISBN:3211836519" Paper_ID="/124464.html" Extracted="3211836519" />

<identifier Org="ISBN:3540715908" Paper_ID="/124464.html" Extracted="3540715908" DDC="005.1" Normalized_DDC="0051" Normalized_Weight="0.25" />

</rec>

<rec ID="/28160.html" Type="article" CiteSeer_Book="Neural Computation" CiteSeer_Volume="7" Title="Regularization Theory and Neural Networks Architectures,">

<identifier Org="ISBN:0198524226" Paper_ID="/28160.html" Extracted="0198524226" DDC="519.5/0285/632" Normalized_DDC="51950285632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:0262112450" Paper_ID="/28160.html" Extracted="0262112450" />

<identifier Org="ISBN:0262201070" Paper_ID="/28160.html" Extracted="0262201070" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.0625" />

<identifier Org="ISBN:0780332113" Paper_ID="/28160.html" Extracted="0780332113" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:0780378989" Paper_ID="/28160.html" Extracted="0780378989" />

<identifier Org="ISBN:0805826084" Paper_ID="/28160.html" Extracted="0805826084" />

<identifier Org="ISBN:0849323592" Paper_ID="/28160.html" Extracted="0849323592" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:1402075324" Paper_ID="/28160.html" Extracted="1402075324" DDC="004/.3" Normalized_DDC="0043" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3211007431" Paper_ID="/28160.html" Extracted="3211007431" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540202277" Paper_ID="/28160.html" Extracted="3540202277" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540228411" Paper_ID="/28160.html" Extracted="3540228411" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540250573" Paper_ID="/28160.html" Extracted="3540250573" DDC="006.312" Normalized_DDC="006312" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540262083" Paper_ID="/28160.html" Extracted="3540262083" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540287558" Paper_ID="/28160.html" Extracted="3540287558" DDC="006.32" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540402101" Paper_ID="/28160.html" Extracted="3540402101" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540404082" Paper_ID="/28160.html" Extracted="3540404082" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540440747" Paper_ID="/28160.html" Extracted="3540440747" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540717005" Paper_ID="/28160.html" Extracted="3540717005" DDC="005.74" Normalized_DDC="00574" Normalized_Weight="0.0625" />

<identifier Org="ISBN:3540746897" Paper_ID="/28160.html" Extracted="3540746897" />

<identifier Org="ISBN:981022270X" Paper_ID="/28160.html" Extracted="981022270X" DDC="006.424" Normalized_DDC="006424" Normalized_Weight="0.0625" />

</rec>

<rec ID="/267997.html" Type="article" CiteSeer_Book="Neural Computation" CiteSeer_Volume="8" Title="Neural Networks for Optimal Approximation of Smooth and Analytic Functions,">

<identifier Org="ISBN:0262100657" Paper_ID="/267997.html" Extracted="0262100657" />

<identifier Org="ISBN:0262194503" Paper_ID="/267997.html" Extracted="0262194503" />

<identifier Org="ISBN:0387954414" Paper_ID="/267997.html" Extracted="0387954414" DDC="519.5/36" Normalized_DDC="519536" Normalized_Weight="0.16666666666666666" />

<identifier Org="ISBN:0521770882" Paper_ID="/267997.html" Extracted="0521770882" />

<identifier Org="ISBN:0780327403" Paper_ID="/267997.html" Extracted="0780327403" />

<identifier Org="ISBN:0780335511" Paper_ID="/267997.html" Extracted="0780335511" />

<identifier Org="ISBN:0780344553" Paper_ID="/267997.html" Extracted="0780344553" />

<identifier Org="ISBN:0792399331" Paper_ID="/267997.html" Extracted="0792399331" DDC="006.3/2/0151" Normalized_DDC="006320151" Normalized_Weight="0.16666666666666666" />

<identifier Org="ISBN:0817643478" Paper_ID="/267997.html" Extracted="0817643478" DDC="551.46/072/7" Normalized_DDC="551460727" Normalized_Weight="0.16666666666666666" />

<identifier Org="ISBN:0849317193" Paper_ID="/267997.html" Extracted="0849317193" />

<identifier Org="ISBN:1402075324" Paper_ID="/267997.html" Extracted="1402075324" DDC="004/.3" Normalized_DDC="0043" Normalized_Weight="0.16666666666666666" />

<identifier Org="ISBN:1880653540" Paper_ID="/267997.html" Extracted="1880653540" />

<identifier Org="ISBN:3540358641" Paper_ID="/267997.html" Extracted="3540358641" DDC="003" Normalized_DDC="003" Normalized_Weight="0.16666666666666666" />

<identifier Org="ISBN:3540423435" Paper_ID="/267997.html" Extracted="3540423435" DDC="006.3/1" Normalized_DDC="00631" Normalized_Weight="0.16666666666666666" />

<identifier Org="ISBN:7302106630" Paper_ID="/267997.html" Extracted="7302106630" />

<identifier Org="ISBN:8573077182" Paper_ID="/267997.html" Extracted="8573077182" />

</rec>

<rec ID="/481511.html" Type="misc" CiteSeer_Book="" CiteSeer_Volume="" Title="Back Propagation in a Clifford Algebra,">

<identifier Org="ISBN:0387951911" Paper_ID="/481511.html" Extracted="0387951911" DDC="006.3/1" Normalized_DDC="00631" Normalized_Weight="0.125" />

<identifier Org="ISBN:0444894888" Paper_ID="/481511.html" Extracted="0444894888" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.125" />

<identifier Org="ISBN:0780319028" Paper_ID="/481511.html" Extracted="0780319028" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.125" />

<identifier Org="ISBN:0780332113" Paper_ID="/481511.html" Extracted="0780332113" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.125" />

<identifier Org="ISBN:0805826084" Paper_ID="/481511.html" Extracted="0805826084" />

<identifier Org="ISBN:1599048493" Paper_ID="/481511.html" Extracted="1599048493" DDC="006.303" Normalized_DDC="006303" Normalized_Weight="0.125" />

<identifier Org="ISBN:1605662143" Paper_ID="/481511.html" Extracted="1605662143" DDC="006.3/2" Normalized_DDC="00632" Normalized_Weight="0.125" />

<identifier Org="ISBN:3540635173" Paper_ID="/481511.html" Extracted="3540635173" DDC="006.3/7" Normalized_DDC="00637" Normalized_Weight="0.125" />

<identifier Org="ISBN:9812384642" Paper_ID="/481511.html" Extracted="9812384642" DDC="006.3" Normalized_DDC="0063" Normalized_Weight="0.125" />

</rec>

<rec ID="SELF" Type="SELF" CiteSeer_Book="SELF" CiteSeer_Volume="SELF" Title="Recent Results and Mathematical Methods for Functional Approximation by Neural Networks" />

</references_metadata>