de Castro L N, Von Zuben F J
Department of Computer Engineering and Industrial Automation, UNICAMP, Campinas, São Paulo, Caixa Postal6101, CEP13081-970, Brasil.
Int J Neural Syst. 2001 Dec;11(6):523-35. doi: 10.1142/S0129065701000941.
The appropriate operation of a radial basis function (RBF) neural network depends mainly upon an adequate choice of the parameters of its basis functions. The simplest approach to train an RBF network is to assume fixed radial basis functions defining the activation of the hidden units. Once the RBF parameters are fixed, the optimal set of output weights can be determined straightforwardly by using a linear least squares algorithm, which generally means reduction in the learning time as compared to the determination of all RBF network parameters using supervised learning. The main drawback of this strategy is the requirement of an efficient algorithm to determine the number, position, and dispersion of the RBFs. The approach proposed here is inspired by models derived from the vertebrate immune system, that will be shown to perform unsupervised cluster analysis. The algorithm is introduced and its performance is compared to that of the random, k-means center selection procedures and other results from the literature. By automatically defining the number of RBF centers, their positions and dispersions, the proposed method leads to parsimonious solutions. Simulation results are reported concerning regression and classification problems.
径向基函数（RBF）神经网络的恰当运行主要取决于对其基函数参数的适当选择。训练RBF网络的最简单方法是假设定义隐藏单元激活的径向基函数是固定的。一旦RBF参数固定，就可以通过使用线性最小二乘算法直接确定最优的输出权重集，这通常意味着与使用监督学习确定所有RBF网络参数相比，学习时间会减少。这种策略的主要缺点是需要一种有效的算法来确定RBF的数量、位置和离散度。这里提出的方法受到源自脊椎动物免疫系统的模型的启发，该模型将被证明可执行无监督聚类分析。介绍了该算法，并将其性能与随机、k均值中心选择程序的性能以及文献中的其他结果进行了比较。通过自动定义RBF中心的数量、位置和离散度，所提出的方法可得出简洁的解决方案。报告了关于回归和分类问题的仿真结果。
