Geodesic
Relative cost curves: An alternative to AUC and an extension to 3-class problems
Kybernetika, Tome 50 (2014) no. 5, pp. 647-660.

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Performance evaluation of classifiers is a crucial step for selecting the best classifier or the best set of parameters for a classifier. Receiver Operating Characteristic (ROC) curves and Area Under the ROC Curve (AUC) are widely used to analyse performance of a classifier. However, the approach does not take into account that misclassification for different classes might have more or less serious consequences. On the other hand, it is often difficult to specify exactly the consequences or costs of misclassifications. This paper is devoted to Relative Cost Curves (RCC) - a graphical technique for visualising the performance of binary classifiers over the full range of possible relative misclassification costs. This curve provides helpful information to choose the best set of classifiers or to estimate misclassification costs if those are not known precisely. In this paper, the concept of Area Above the RCC (AAC) is introduced, a scalar measure of classifier performance under unequal misclassification costs problem. We also extend RCC to multicategory problems when misclassification costs depend only on the true class.
DOI : 10.14736/kyb-2014-5-0647
Classification : 62A10, 62N05, 93E12
Keywords: classifier; performance evaluation; misclassification costs; cost curves; ROC curves; AUC 
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     title = {Relative cost curves: {An} alternative to {AUC} and an extension to 3-class problems},
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Montvida, Olga; Klawonn, Frank. Relative cost curves: An alternative to AUC and an extension to 3-class problems. Kybernetika, Tome 50 (2014) no. 5, pp. 647-660. doi : 10.14736/kyb-2014-5-0647. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-5-0647/

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