Modeling of fuzzy systems by ellipsoidal partitions of input/output space

In this paper, a GA based ellipsoid learning algorithm is proposed for fuzzy modeling. Since the conventional Gustafson-Kessel algorithm (GKA) is an effective method for the clustering of data points but not suitable for estimating the distribution of data points belonging to the same cluster, GA is employed along with GKA to learn the optimal size as well as the parameters of ellipsoids. As the prototype input/output data points are clustered by ellipsoids, it is considered as the first stage coarse learning of fuzzy modeling. An efficient method is proposed transforming all the parameters of ellipsoids into initial conditions for the second stage gradient descent method to improve the convergence of gradient descent method.