A better Beta for the H measure of classification performance

Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ Abstract The area under the ROC curve is widely used as a measure of performance of classification rules. However, it has recently been shown that the measure is fundamentally incoherent, in the sense that it treats the relative severities of misclassifications differently when different classifiers are used. To overcome this, [5, 6] proposed the H measure, which allows a given researcher to fix the distribution of relative severities to a classifier-independent setting on a given problem. Keywords: supervised classification, classifier performance, AUC, ROC curve, H measure 1. Introduction The aim of supervised classification is to construct a rule which will allow one to assign objects to one of M classes, on the basis of vectors of descriptive features of those objects. The rule will be constructed using a'training' set (machine learning and pattern recognition terminology) or'design' set (statistics terminology) of data which includes both descriptive vectors and true classes for a sample of objects.