On the multistage Bayes classifier

Abstract

This paper deals with the decision rules of a multistage classifier based on a decision tree scheme. For the given tree skeleton and features to be used, the optimal (Bayes) decision rules (strategy) for performing the classification at each nonterminal node are derived and discussed. Since, in a general case, the risk minimization leads to the involved (inseparable by analytical methods) optimal decision rules, the separability problem of multistage recognition strategy is discussed and sufficient conditions for the separability of the multistage Bayes classifier are given. The separable suboptimal strategy is proposed and compared with the optimal one in respect of classification accuracy. The primary results are illustrated by simple examples.