Analysis of proposed three-class classification decision rules in terms of the ideal observer decision rule

We analyze recently proposed decision rules for three-class classification from the point of view of ideal observer decision theory. We consider three-class decision rules proposed by Scurfield, by Chan et al., and by Mossman. Scurfield's decision rule is shown to be a special case of the three-class ideal observer decision rule in three different situations. Chan et al. start with an ideal observer model and specify its decision-consequence utility structure in a way that causes two of the decision lines used by the ideal observer to overlap and the third line to become undefined. Finally, we show that, for a particular and obvious choice of ideal-observer-related decision variables, the Mossman decision rule cannot be a special case of the ideal observer decision rule. Despite the considerable difficulties presented by the three-class classification task, the three-class ideal observer provides a useful framework for analyzing a variety of three-class decision strategies.