Why Cohen’s Kappa should be avoided as performance measure in classification

English version

Autoři: Rosario Delgado ^aff001; Xavier-Andoni Tibau ^aff002
Působiště autorů: Department of Mathematics, Universitat Autònoma de Barcelona, Campus de la UAB, Cerdanyola del Vallès, Spain ^aff001; Advanced Stochastic Modelling research group, Universitat Autònoma de Barcelona, Campus de la UAB, Cerdanyola del Vallès, Spain ^aff002
Vyšlo v časopise: PLoS ONE 14(9)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0222916

Souhrn

We show that Cohen’s Kappa and Matthews Correlation Coefficient (MCC), both extended and contrasted measures of performance in multi-class classification, are correlated in most situations, albeit can differ in others. Indeed, although in the symmetric case both match, we consider different unbalanced situations in which Kappa exhibits an undesired behaviour, i.e. a worse classifier gets higher Kappa score, differing qualitatively from that of MCC. The debate about the incoherence in the behaviour of Kappa revolves around the convenience, or not, of using a relative metric, which makes the interpretation of its values difficult. We extend these concerns by showing that its pitfalls can go even further. Through experimentation, we present a novel approach to this topic. We carry on a comprehensive study that identifies an scenario in which the contradictory behaviour among MCC and Kappa emerges. Specifically, we find out that when there is a decrease to zero of the entropy of the elements out of the diagonal of the confusion matrix associated to a classifier, the discrepancy between Kappa and MCC rise, pointing to an anomalous performance of the former. We believe that this finding disables Kappa to be used in general as a performance measure to compare classifiers.

Klíčová slova:

Entropy – Machine learning – Medicine and health sciences – Probability distribution – Protein structure prediction – Psychology – Statistical distributions – Covariance

Zdroje

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Why Cohen’s Kappa should be avoided as performance measure in classification

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