Not all classification problems involve binary targets. For example, color researchers may be interested in user classification of colors such as red, blue, yellow, green, and so on. In earlier chapters, we dealt with cost-benefit analysis for classification models having a binary target variable only. In this chapter, we extend our analytic framework to encompass classification evaluation measures and data-driven misclassification costs, first for trinary targets, and then for k-nary targets in general.
For the classification problem with a generic trinary target variable taking values A, B, and C, there are nine possible combinations of predicted/actual categories, as shown in Table 17.1. The contingency table for this generic trinary problem is as shown in Table 17.2.
Table 17.1 Definition and notation for the nine possible decision combinations, generic trinary variable