Approximation by Ridge Functions and Neural Networks
SOUTH CAROLINA UNIV COLUMBIA COLUMBIA
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We investigate the efficiency of approximation by linear combinations of ridge functions... Thus the theorems we obtain show that this form of ridge approximation has the same efficiency of approximation as other more traditional methods of multivariate approximation such as polynomials splines or wavelets The theorems we obtain can be applied to show that a feed forward neural network with one hidden layer of computational nodes given by certain sigmoidal function sigma will also have this approximation efficiency. Minimal requirements are made of the sigmoidal functions and in particular our results hold for the unit impulse function.
- Numerical Mathematics