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- Title
VUS and HUM Represented with Mann-Whitney Statistic.
- Authors
Chong Sun Hong; Min Ho Cho
- Abstract
The area under the ROC curve (AUC), the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) are defined and interpreted with probability that measures the discriminant power of classification models. AUC, VUS and HUM are expressed with the summation and integration notations for discrete and continuous random variables, respectively. AUC for discrete two random samples is represented as the nonparametric Mann-Whitney statistic. In this work, we define conditional Mann-Whitney statistics to compare more than two discrete random samples as well as propose that VUS and HUM are represented as functions of the conditional Mann-Whitney statistics. Three and four discrete random samples with some tie values are generated. Values of VUS and HUM are obtained using the proposed statistic. The values of VUS and HUM are identical with those obtained by definition; therefore, both VUS and HUM could be represented with conditional Mann-Whitney statistics proposed in this paper.
- Subjects
RECEIVER operating characteristic curves; GRAPHIC methods for multivariate analysis; SENSITIVITY &; specificity (Statistics); NONPARAMETRIC statistics; MATHEMATICAL statistics
- Publication
Communications for Statistical Applications & Methods, 2015, Vol 22, Issue 3, p223
- ISSN
2287-7843
- Publication type
Article
- DOI
10.5351/CSAM.2015.22.3.223