A weighted grey CMAC neural network with output differentiability

The Cerebellar Model Arithmetic Computer (CMAC) is a table lookup neurocomputing technique. It can be viewed as a basis function network (BFN) and performs well in terms of its fast learning speed, local generalization capability for approximating nonlinear functions. However, a disvantage is that the derivative of its output cannot be preserved due to the CMAC uses a constant basis function within each quantized state. This creates the limitation and inconvenience while the derivative information is needed in real-world applications. This paper proposes a Weight Grey CMAC (WGCMAC) that includes the conventional CMAC weight addressing scheme and the weighted grey prediction model to resolve this problem. Based on the weighted grey prediction model, we present an efficient learning algorithm for the proposed WGCMAC. Experiments confirm that the WGCMAC not only has a faster learning speed than the conventional CMAC, but also provides output derivatives and more precise learning result. Besides, compared with other enhanced CMAC models providing output derivatives, the proposed method has fastest learning speed.