Publication | Closed Access
Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks
3.4K
Citations
0
References
1988
Year
Numerical AnalysisArtificial IntelligenceIncremental LearningGeometric LearningEngineeringMachine LearningGreat BritainFunctional AnalysisData ScienceComputational GeometryApproximation TheoryGeometric ModelingInterpolation SpaceComputational Learning TheoryMulti-variable Functional InterpolationAdaptive Layered NetworksComputer ScienceAdaptive AlgorithmNonlinear Dimensionality ReductionMultivariate ApproximationRadial Basis FunctionFunctional Data AnalysisInterpolation Scheme ExplicitNatural Sciences
The relationship between learning in adaptive layered networks and fitting high‑dimensional surfaces is explored, framing generalization as interpolation between known data points and suggesting a rational theory for such networks. The authors identify a class of adaptive networks that make the interpolation scheme explicit. This class explicitly implements interpolation between known data points. The networks learn by solving linear equations, enabling representation of nonlinear relationships with a guaranteed learning rule. Great Britain.
Abstract : The relationship between 'learning' in adaptive layered networks and the fitting of data with high dimensional surfaces is discussed. This leads naturally to a picture of 'generalization in terms of interpolation between known data points and suggests a rational approach to the theory of such networks. A class of adaptive networks is identified which makes the interpolation scheme explicit. This class has the property that learning is equivalent to the solution of a set of linear equations. These networks thus represent nonlinear relationships while having a guaranteed learning rule. Great Britain.