On the Capacity of Feed-forward Neural Networks for Fuzzy Classification

Abstract-This paper investigates the ability of feed-forward neural network (FFNN) classifiers trained with examples to generalize and estimate the structure of the feature space in the form of class membership information. A functional theory of FFNN classifiers is developed from formal definitions. The properties of discriminant functions learned by FFNN classifiers from sample data are also studied. These properties show that the ability of FFNNs to identify and quantify uncertainty in a feature space is sensitively dependent on the topology of the feature space and that FFNNs trained to classify overlapping classes of data tend to create sharp transitions between closely spaced feature vectors belonging to different classes.