Kernel CMAC With Improved Capability

Abstract

The cerebellar model articulation controller (CMAC) has some attractive features, namely fast learning capability and the possibility of efficient digital hardware implementation. Although CMAC was proposed many years ago, several open questions have been left even for today. The most important ones are about its modeling and generalization capabilities. The limits of its modeling capability were addressed in the literature, and recently, certain questions of its generalization property were also investigated. This paper deals with both the modeling and the generalization properties of CMAC. First, a new interpolation model is introduced. Then, a detailed analysis of the generalization error is given, and an analytical expression of this error for some special cases is presented. It is shown that this generalization error can be rather significant, and a simple regularized training algorithm to reduce this error is proposed. The results related to the modeling capability show that there are differences between the one-dimensional (1-D) and the multidimensional versions of CMAC. This paper discusses the reasons of this difference and suggests a new kernel-based interpretation of CMAC. The kernel interpretation gives a unified framework. Applying this approach, both the 1-D and the multidimensional CMACs can be constructed with similar modeling capability. Finally, this paper shows that the regularized training algorithm can be applied for the kernel interpretations too, which results in a network with significantly improved approximation capabilities.