Title: Multivariate interpolation using radial basis function networks

Authors: Dang Thi Thu Hien, Hoang Xuan Huan, Huu Tue Huynh

Addresses: Faculty of Information Technology, University of Transport and Communications, Hanoi, Vietnam, LangThuong Wd., DongDa Dist., Hanoi City, Vietnam. ' Faculty of Information Technology, College of Technology, Vietnam National University, Hanoi, 144 XuanThuy Rd., CauGiay Dist., Hanoi City, Vietnam. ' Bacha International University, Hanoi, Vietnam, 103 D5, Lot C, NguyenPhongSac Rd., DichvongHau Wd, Caugiay Dist., Hanoi City, Vietnam

Abstract: There is, hitherto, no efficient method to interpolate multivariate functions, for especially dynamic problems in which new training data are often added in real-time. In order to construct an efficient method, this paper considers local interpolation RBF networks, where artificial neural network approach and instance-based learning are combined. In these networks, training data are clustered into relatively small sub-clusters and on each sub-cluster, an interpolation RBF network is trained by using a new algorithm recently proposed by the authors; it is a two-phase algorithm for training interpolation RBF networks using Gaussian basis functions and it has the complexity O(N²), where N is the number of nodes. The training time of this new architecture is effectively short and its generality is superior to global RBF networks. Furthermore its universal approximation property is proven. Especially, this new architecture can be efficiently used for dynamic training.

Keywords: radial basis functions; RBFs; width parameters; output weights; contraction transformation; k-d tree; local interpolation; RBF networks; artificial neural networks; ANNs; instance-based learning; multivariate interpolation.

DOI: 10.1504/IJDMMM.2009.027287

International Journal of Data Mining, Modelling and Management, 2009 Vol.1 No.3, pp.291 - 309

Published online: 19 Jul 2009 *

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