Abstract
We study approximation problems formulated as regularized minimization problems with kernel-based stabilizers. These approximation schemas exhibit easy derivation of solution to the problem in the shape of linear combination of kernel functions (one-hidden layer feed-forward neural network schemas). We prove uniqueness and existence of solution to the problem. We exploit the article by N. Aronszajn [1] on reproducing kernels and use his formulation of product of kernels and resulting kernel space to derive a new approximation schema — a Product Kernel Regularization Network. We present a concrete application of PKRN and compare it to classical Regularization Network and show that PKRN exhibit better approximation properties.
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Petra, K., Terezie, Š. (2005). Product Kernel Regularization Networks. In: Ribeiro, B., Albrecht, R.F., Dobnikar, A., Pearson, D.W., Steele, N.C. (eds) Adaptive and Natural Computing Algorithms. Springer, Vienna. https://doi.org/10.1007/3-211-27389-1_104
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DOI: https://doi.org/10.1007/3-211-27389-1_104
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-24934-5
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