Review of several proposed three-class classification decision rules and their relation to the ideal observer decision rule

摘要

We analyzed a variety of recently proposed decision rules for three-class classification from the point of view ofideal observer decision theory. We considered three-class decision rules which have been proposed recently: oneby Scurfield, one by Chan et al., and one by Mossman. Scurfield’s decision rule can be shown to be a specialcase of the three-class ideal observer decision rule in two different situations: when the pair of decision variablesis the pair of likelihood ratios used by the ideal observer, and when the pair of decision variables is the pair oflogarithms of the likelihood ratios. Chan et al. start with an ideal observer model, where two of the decisionlines used by the ideal observer overlap, and the third line becomes undefined. Finally, we showed that theMossman decision rule (in which a single decision line separates one class from the other two, while a second lineseparates those two classes) cannot be a special case of the ideal observer decision rule. Despite the considerabledifficulties presented by the three-class classification task compared with two-class classification, we found thatthe three-class ideal observer provides a useful framework for analyzing a wide variety of three-class decisionstrategies.