A Nonparametric Approach to Pattern Recognition. Part I. The Locally Disjoint Case

摘要

A mathematically rigorous procedure is developed which transforms the underlying unknown probability structure of a pattern discrimination problem to the real line. This transformed probability space is then partitioned using the fact that the locations of the relative extrema of the difference of empirical distribution functions will converge to the boundaries of the likelihood decision rule. In Part I, a method is proposed based on the locations of the relative extrema for discriminating between two disjoint pattern classes. It is shown that this procedure will produce perfect discrimination with probability 1. (When the classes are locally disjoint (defined in the text), perfect discrimination is possible with only a finite learning phase). In Part II this procedure is modified to include the non-disjoint case. (Author)