高阶CMAC神经网络的研究

RESEARCH ON A HIGH ORDER CMAC NEURAL NETWORK

提出了一种高阶ＣＭＡＣ（ＨＣＭＡＣ）神经网络．它是采用高阶的径向基函数作为接收域函数，为了进一步增强对输入模式的表达，还可以用接收域函数与输入模式向量构成张量积，这时产生的是高维的增强表达，同时ＨＣＭＡＣ沿用ＣＭＡＣ的地址映射方法．由于高阶接收域函数的引入，使其可以获得较ＣＭＡＣ连续性强且有解析微分的复杂函数近似．ＨＣＭＡＣ在不改变ＣＭＡＣ简单结构的基础上较ＲＢＦ网络有计算量少，学习效率高等优点．文中还首次将用于参数估计的Ｋａｌｍａｎ滤波学习算法引入到这种类ＣＭＡＣ的网络学习中，这使ＨＣＭＡＣ有更高的学习速度．通过仿真研究表明ＨＣＭＡＣ除拥有ＣＭＡＣ和ＲＢＦ网络两者的优点外。

In this paper, a high order CMAC(HCMAC) neural network is proposed, in which the high order activation functions are utilized as the receptive field functions. The method of address mapping used by CMAC is adopted in the new network. Because of enhancement of the input pattern, the physical address in HCMAC is reduced highly, and by using HCMAC the approximation of complex functions can be obtained which is more continuous than using CMAC and has analytic derivatives. As a result of these characters, the computing amount and learning time are reduced more than RBF neural networks. This paper also introduces originally the Kalman filter algorithm to the CMAC like networks, so learning effectiveness is improved further. By simulating, it is proved that HCMAC is feasible in many fields.