The need for function approximations arises in many branches of applied mathematics, and computer science in particular.
Function approximation:
The tasks of function approximation is to find an estimate of the unknown function f() subject to noise. Various engineering and scientific disciplines require function approximation.
Function Approximation The task of finding an instance from a class of functions that is minimally different from an unknown function. This is a common task for neural networks.
function approximation algorithms include connectionist and statistical techniques of machine learning.
Function approximation
Time series prediction
Classification
Pattern recognition ...
Instead, function approximation may be useful to construct components of pathfinding. It may be that the movement cost function is unknown.
Support vector method for function approximation, regression estimation, and signal processing. In M. Mozer, M. Jordan, and T. Petsche, editors, Advances in Neural Information Processing Systems 9, pages 281- 287, Cambridge, MA, 1997. MIT Press.
By thresholding the output value, a classifier can be constructed (such as Widrow's Adaline), but here we focus on the linear relationship and use the network for a function approximation task.
To use a neural network for classification, we need to construct an equivalent function approximation problem by assigning a target value for each class.
It does not work very well with function approximation and there have been reports that a better version is under development that will work well on function approximation problems and be simpler as well.
None of this is specific to RBF networks, and the same could be said about any function approximation technique. So why RBF networks ?
Why RBF networks ?
Friedman, J. H. (1999a). Greedy function approximation: A gradient boosting machine. IMS 1999 Reitz Lecture.
Neural Dot Net Pt 7 The BackPropagation Network demos for comparing #s and words (also has Adaline and SOM NNs)
C# Neural network library - demos for facial recognition!, function approximation, and repartition ...
This tutorial will cover Markov decision processes and approximate value functions as the formulation of the reinforcement learning problem, and temporal-difference learning, function approximation, ...
Currently, we are planning to cover signal processing and function approximation applications of the discrete Fourier transform and singular value decomposition.
"Hoeffding Races: Accelerating Model Selection Search for Classification and Function Approximation"
"Efficient Algorithms for Minimizing Cross Validation Error"
"Note on free lunches and cross-validation" ...
 See also: Neural network, Classification, Percept, Perceptron, Machine learning
  
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