Hybrid fuzzy ellipsoidal learning

Desribes a hybrid system which combines supervised and unsupervised learning to find and tune the fuzzy-rule ellipsoids. Supervised learning tunes the ellipsoids to improve the approximation. Unsupervised competitive learning finds the statistics of data clusters. The covariance matrix of each synaptic quantization vector defines an ellipsoid centered at the quantizing vector or centroid of the data cluster. Tightly clustered data gives smaller ellipsoids or more certain rules. Sparse data gives larger ellipsoids or less certain rules. The supervised neural system learns with gradient descent to find the ellipsoidal fuzzy patches. It locally minimizes the mean-squared error of the fuzzy approximation. The hybrid system gives a more accurate approximation than either the supervised or unsupervised system.