Eigenanalysis of CMAC neural network

Abstract

The CMAC neural network is by itself an adaptive processor. This paper studies the CMAC algorithm from the point of view of adaptive filter theory. Correspondingly, the correlation matrix is defined and the Wiener-Hopf equation is obtained for the CMAC neural network. It is revealed that the trace (i.e., sum of eigenvalues) of the correlation matrix is equal to the generalization parameter of the CMAC neural network. Using the tool of eigenanalysis, analytical bounds of the learning rate of CMAC neural network are derived which guarantee convergence of the weight vector in the mean. Moreover, a simple formula of estimating the misadjustment due to the gradient noise is derived. © Springer-Verlag Berlin Heidelberg 2005.