Generalization Improvement of a Fuzzy Classifier With Ellipsodial Regions

In a fuzzy classifier with ellipsoidal regions, each cluster is approximated by a center and a covariance matrix, and the membership function is calculated using the inverse of the covariance matrix. Thus when the number of training data is small, the covariance matrix becomes singular and the generalization ability is degraded. In this paper, during the symmetric Cholesky factorization of the covariance matrix, if the input of the square root is smaller than a prescribed positive value, we replace the input with the prescribed value. Further, we tune the slopes of the membership functions so that the margins are maximized. We show the validity of our method by computer simulations.