The pattern discrimination problem from the perspective of relation theory

摘要

Pattern discrimination is viewed from the perspective of relation theory. Measurement data is a binary relation from the set of units to the set of measurements and the category identification data is a binary relation from the set of units to the set of categories. The decision rule is a binary relation from the set of measurements to the set of categories. First, no structure is assumed on the set of measurements or the set of units and the form of the optimal decision relation is determined for the case of unit independence. Then a binary relation dependence structure is assumed on the set of units and two approximating forms of decision relations are determined. The approximating decision relation for the unit dependence case has a distinctive form quite different from the decision rule which would result from the usual Markov dependence assumption. It is hoped that relation model for pattern discrimination can provide a useful complementary alternative to the statistical model currently in use.