Refining the performance metrics and related mathematical operators for ordinal classification problems

In multilabel classification (MLC) problems, the standard confusion matrix is generally replaced by a set of confusion matrices, with one matrix per label. Although ordinal classification problems are slightly different from MLC, it shares the same set of performance metrics used for MLC. We contend that ordinal classification has nuances which makes it different from MLC. As in binary classification, the notion of false positive and false negative are still valid in MLC problems in a sense that any wrongly predicted label can be termed as false positive (or false negative). However, in ordinal classification, these notions are replaced by overestimates and underestimates. We propose the use of different mathematical operators to quantify the strength of overestimates and underestimates. The proposed metrics tailored for ordinal classifiers not only introduces a novel framework for evaluation but also signifies a crucial step forward in enhancing the performance evaluation of ordinal classification algorithms. We demonstrate its practical usefulness with the help of a number of case studies.