基于快速密度聚类的RBF神经网络设计

针对径向基函数（radial basis function，RBF）神经网络隐含层结构难以确定的问题，提出一种基于快速密度聚类的网络结构设计算法。该算法将快速密度聚类算法良好的聚类特性用于RBF神经网络结构设计中，通过寻找密度最大的点并将其作为隐含层神经元，进而确定隐含层神经元个数和初始参数；同时，引入高斯函数的特性，保证了每个隐含层神经元的活性；最后，用一种改进的二阶算法对神经网络进行训练，提高了神经网络的收敛速度和泛化能力。利用典型非线性函数逼近和非线性动态系统辨识实验进行仿真验证，结果表明，基于快速密度聚类设计的RBF神经网络具有紧凑的网络结构、快速的学习能力和良好的泛化能力。

Construction of RBF neural networks via fast density clustering

To design a hidden layer structure in radial-basis-function (RBF) neural networks, a novel algorithm based on fast density clustering is proposed. The algorithm searches for the point with the highest density and then uses it as the neuron of the hidden layer, thereby ascertaining the number of neurons in the hidden layer and the initial parameters. Moreover, the activity of each hidden neuron is ensured by introducing the Gaussian function. An improved second-order algorithm is used to train the designed network, increasing the training speed and improving the generalization performance. In addition, two benchmark simulations-the typical nonlinear function approximation and the nonlinear dynamic system identification experiment -are used to test the effectiveness of the proposed RBF neural network. The results suggest that the proposed RBF neural network based on fast density clustering offers improved generalization performance, has a compact structure, and requires shorter training time.