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.