Parametric CMAC networks: Fundamentals and applications of a fast convergence neural structure

This work shows fundamentals and applications of the Parametric CMAC (P-CMAC) network a neural structure derived from Albus CMAC algorithm and Takagi-Sugeno-Kang parametric fuzzy inference systems. It resembles the original CMAC proposed by James Albus in the sense that it is a local network, i.e., for a given input vector, only a few of the networks nodes (or neurons) will be active and will effectively contribute to the corresponding network output. The internal mapping structure is built in such a way that it implements, for each CMAC memory location, one linear parametric equation of the network input strengths. This mapping can be thought of as the corresponding of a hidden layer in a multi-layer perceptron (MLP) structure. The output of the active equations are then weighted and averaged to generate the actual outputs to the network. A practical comparison between the proposed network and other structures is accomplished. P-CMAC, MLP and CMAC networks are applied to approximate a nonlinear function. Results show advantages of the proposed algorithm, based on the computational efforts needed by each network to perform nonlinear function approximation. Also, P-CMAC is used to solve a practical problem at mobile telephony, approximating a RF mapping at a given region to help operational people while maintaining service quality.