An improved multi-dimensional CMAC neural network: Receptive field function and placement

Abstract

The standard CMAC has been shown to have fast learning computation as a result of modular receptive field placement, rectangular receptive field shape and a simple weight adaptation algorithm. The standard CMAC, however, suffers from slow convergence at some critical frequency due to the rectangular receptive field shape. A linearly-tapered field, which requires a uniform placement, was used in this research. The receptive field placement of the standard CMAC becomes less uniform locally for a larger receptive field width. This dissertation suggests a new field placement which is more uniform without extra computation. Results show that the slow convergence at the critical frequency is eliminated, and the interaction of the linearly-tapered field with the new placement achieves more accurate function approximation. A theoretical bound on the receptive field width as a function of the input dimension is proposed if a uniform placement is to be achieved. Also, a procedure for adapting receptive field density to minimize the weight usage for a given approximation accuracy is suggested