Potential Functions in Mathematical Pattern Recognition

This paper discusses a class of methods for pattern classification using a set of samples. They may also be used in reconstructing a probability density from samples. The methods discussed are potential function methods of a type directly derived from concepts related to superposition. The characteristics required of a potential function are examined, and it is shown that smooth potential functions exist that will separate arbitrary sets of sample points. Ideas suggested by Specht in regard to polynomial potential functions are extended.