By Ivan Bratko (auth.), Andrej Dobnikar, Uroš Lotrič, Branko à ter (eds.)
The two-volume set LNCS 6593 and 6594 constitutes the refereed complaints of the tenth foreign convention on Adaptive and typical Computing Algorithms, ICANNGA 2010, held in Ljubljana, Slovenia, in April 2010. The eighty three revised complete papers offered have been rigorously reviewed and chosen from a complete of one hundred forty four submissions. the 1st quantity contains forty two papers and a plenary lecture and is equipped in topical sections on neural networks and evolutionary computation.
Read or Download Adaptive and Natural Computing Algorithms: 10th International Conference, ICANNGA 2011, Ljubljana, Slovenia, April 14-16, 2011, Proceedings, Part I PDF
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Additional info for Adaptive and Natural Computing Algorithms: 10th International Conference, ICANNGA 2011, Ljubljana, Slovenia, April 14-16, 2011, Proceedings, Part I
Neurocomputing 74, 401–417 (2010) 5. : A family of model predictive control algorithms with artiﬁcial neural networks. International Journal of Applied Mathematics and Computer Science 17, 217–232 (2007) 6. : Predictive control with constraints. Prentice Hall, Harlow (2002) 7. : Application of fuzzy Wiener models in eﬃcient MPC algorithms. , Hu, Q. ) RSCTC 2010. LNCS (LNAI), vol. 6086, pp. 669–677. Springer, Heidelberg (2010) 8. : Neural networks for modelling and control of dynamic systems. Springer, London (2000) 9.
Originally, they considered as stabilizers weighted Fourier transform of the form fˆ(s)2 1 ds , later Girosi  realized that such stabilizers are squares ˆ (2π)d/2 S k(s) of norms on RKHSs as stated in Theorem 1. We denote by Ez,α,K := Ez + α . 2 K (3) the regularized empirical error with the stabilizer . 2K and the regularization parameter α. The next theorem characterizes argminima of Ez and its regularization. The theorem was proven in  by methods from theory of inverse problems. Several authors [18,7,8] proved the part (ii) earlier using Fréchet derivatives.
The next theorem summarizes some properties of Gaussian kernel models; for (i), see Mhaskar ; for (ii) Kůrková and Neruda ; (iii) follows from (ii). Theorem 5. Let d be a positive integer and X ⊂ Rd be compact. Then (i) for all a > 0, span GKγa (X)and HKγa (X)are dense subspaces of (C(X), . d d (ii) the set FKγd (Rd ) = a>0 GKγa (Rd ) is linearly independent; d (iii) for all a, b > 0 such that a = b, span GKγa (Rd ) span GKγb (Rd ) = ∅. d d sup ); 20 V. C. Kainen By Proposition 2, for any width a > 0, all argminima of Ez over the RKHS HKγa (X) induced by the Gaussian kernel with the width a > 0 are also argmind ima of Ez over the whole space C(X).