A Piecewise Linear Network Classifier

A piecewise linear network is discussed which classifies N-dimensional input vectors. The network uses a distance measure to assign incoming input vectors to an appropriate cluster. Each cluster has a linear classifier for generating class discriminants. A training algorithm is described for generating the clusters and discriminants. Theorems are given which relate the network's performance to that of nearest neighbor and k-nearest neighbor classifiers. It is shown that the error approaches Bayes error as the number of clusters and patterns per cluster approach infinity.