CMAC 算法收敛性分析及泛化能力研究

利用矩阵理论和线性方程组迭代收敛的一般性原理，在不附加特殊条件折情况下，证明了CMAC算法在批量和增量两种学习方式下的收敛定理，对在关联矩阵正定条件下得出的结论进行推广和改进。在此基础上提出了一种学习率自寻优的CMAC改进算法，并提出一种简单可行的评价CMAC网络整体泛化性能的指标，通过计算仿真验证了收敛定量的正确性和改进算法的优越性，并研究得出了CMAC网络各个参数对其泛化性能影响的相关结论。

Convergence and Generalization Ability of CMAC

Using the matrix theory and general principle of the iterative convergence of the linear coupled equations, the convergent theorems of the CMAC algorithm are proved both in the batch and the incremental learning styles without any special conditions attached. Some existing conclusions under the condition that the articulation matrix is positive definite are improved. An improved CMAC algorithm of self optimizing learning rate is presented. Moreover, a simple and feasible criterion is presented to evaluate the generalization ability of the whole CMAC network. Simulation results show the correctness of the convergent theorems and the advantages of improved algorithm.