Zero-Error Density Maximization Based Learning Algorithm for a Neuro-Fuzzy Inference System

This paper proposes a novel sequential learning algorithm based on zero-density maximization and extended Kalman filter, together referred to as ZDM-EKF, for a Takagi-Sugeno-Kang fuzzy inference system. The sequential learning begins with zero rules, and rules are added/pruned or updated based on the knowledge contained in the network and prediction error of the current sample. As each sample is presented to the network, the network monitors the spherical potential and mean-squared error and either adds a new rule or updates the parameters of the nearest rules employing an extended Kalman filtering scheme. The Kalman filter estimates the optimal network parameter based on maximizing the error density at origin. This results in a simple and efficient cost function with better ability to learn higher-order statistical behavior in comparison to error based cost function. The performance of the proposed ZDM-EKF based learning algorithm is evaluated on a set of four synthetic function approximation as well as time-series prediction problems. The performance analysis indicates superior performance of the proposed algorithm.i