Neural classifiers using one-time updating

The linear threshold element, or perceptron, is a linear classifier with limited capabilities due to the problems arising when the input pattern set is linearly nonseparable. Assuming that the patterns are presented in a sequential fashion, we derive a theory for the detection of linear nonseparability as soon as it appears in the pattern set. This theory is based on the precise determination of the solution region in the weight spare with the help of a special set of vectors. For this region, called the solution cone, we present a recursive computation procedure which allows immediate detection of nonseparability. The algorithm can be directly cast into a simple neural-network implementation. In this model the synaptic weights are committed. Finally, by combining many such neural models we develop a learning procedure capable of separating convex classes.