Huan Hoang Xuan, Hien Dang Thi Thu, Tue Huynh Huu
College of Technology, Vietnam National University, Hanoi, Vietnam.
IEEE Trans Neural Netw. 2011 Jun;22(6):982-8. doi: 10.1109/TNN.2011.2120619. Epub 2011 May 10.
This brief paper proposes a new algorithm to train interpolation Gaussian radial basis function (RBF) networks in order to solve the problem of interpolating multivariate functions with equally spaced nodes. Based on an efficient two-phase algorithm recently proposed by the authors, Euclidean norm associated to Gaussian RBF is now replaced by a conveniently chosen Mahalanobis norm, that allows for directly computing the width parameters of Gaussian radial basis functions. The weighting parameters are then determined by a simple iterative method. The original two-phase algorithm becomes a one-phase one. Simulation results show that the generality of networks trained by this new algorithm is sensibly improved and the running time significantly reduced, especially when the number of nodes is large.
本文简要提出了一种新的算法来训练插值高斯径向基函数（RBF）网络，以解决在等距节点上对多元函数进行插值的问题。基于作者最近提出的一种高效的两阶段算法，现在将与高斯RBF相关的欧几里得范数替换为方便选择的马氏范数，这使得可以直接计算高斯径向基函数的宽度参数。然后通过一种简单的迭代方法确定加权参数。原来的两阶段算法变成了单阶段算法。仿真结果表明，用这种新算法训练的网络的通用性得到了显著提高，运行时间显著减少，特别是在节点数量较大时。
