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

Abstract

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