Abstract
An approximation result is given concerning gaussian radial basis functions in a general inner-product space. Applications are described concerning the classification of the elements of disjoint sets of signals, and also the approximation of continuous real functions defined on all of ℝ n using RBF networks. More specifically, it is shown that an important large class of classification problems involving signals can be solved using a structure consisting of only a generalized RBF network followed by a quantizer. It is also shown that gaussian radial basis functions defined on ℝ n can uniformly approximate arbitrarily well over all of ℝ n any continuous real functional f on ℝ n that meets the condition that ∣ f(x) ∣ → 0 as ∥x∥ → ∞.
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Sandberg, I.W. (2001). Gaussian Radial Basis Functions and Inner-Product Spaces. In: Dorffner, G., Bischof, H., Hornik, K. (eds) Artificial Neural Networks — ICANN 2001. ICANN 2001. Lecture Notes in Computer Science, vol 2130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44668-0_25
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DOI: https://doi.org/10.1007/3-540-44668-0_25
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