A Fuzzy Classifier with Directed Initialization Adaptive Learning of Norm Inducing Matrix

A fuzzy classifier with adaptive learning of the volume of norm inducing matrix is proposed in this paper. The proposed fuzzy classifier improves the Gustafson-Kessel algorithm (GKA) which assumes a fixed volume of the norm inducing matrix. An efficient approach based on gradient descent learning, called adaptive ellipsoid classification algorithm (AECA) is proposed to recursively update the volume of norm inducing matrix. Mathematical analyses and computer simulations are made to show the effectiveness and efficiency of the proposed fuzzy classifier.