David J. Hand

David J. Hand, Peter Christen, Sumayya Ziyad

The problem of identifying to which of a given set of classes objects belong is ubiquitous, occurring in many research domains and application areas, including medical diagnosis, financial decision making, online commerce, and national security. But such assignments are rarely completely perfect, and classification errors occur. This means it is necessary to compare classification methods and algorithms to decide which is ``best'' for any particular problem. However, just as there are many different classification methods, so there are many different ways of measuring their performance. It is thus vital to choose a measure of performance which matches the aims of the research or application. This paper is a contribution to the growing literature on the relative merits of different performance measures. Its particular focus is the critical importance of matching the properties of the measure to the aims for which the classification is being made.

David J. Hand, Peter Christen, Nishadi Kirielle

The F-measure, also known as the F1-score, is widely used to assess the performance of classification algorithms. However, some researchers find it lacking in intuitive interpretation, questioning the appropriateness of combining two aspects of performance as conceptually distinct as precision and recall, and also questioning whether the harmonic mean is the best way to combine them. To ease this concern, we describe a simple transformation of the F-measure, which we call F* (F-star), which has an immediate practical interpretation.

David J. Hand, Christoforos Anagnostopoulos

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, Hand (2009) 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. This note extends the discussion, and proposes a modified standard distribution for the $H$ measure, which better matches the requirements of researchers, in particular those faced with heavily unbalanced datasets, the $Beta(π_1+1,π_0+1)$ distribution. [Preprint submitted at Pattern Recognition Letters]