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Partial VUS and optimal thresholds
Journal of the Korean Data & Information Science Society 2019;30:895-905
Published online July 31, 2019;
© 2019 Korean Data and Information Science Society.

Chong Sun Hong1 · Min Sub Jung2 · Hye Soo Shin3

123Department of Statistics, Sungkyunkwan University
Correspondence to: Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail:
Received May 10, 2019; Revised June 3, 2019; Accepted June 3, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Based on many literature for the partial VUS (volume under the ROC surface), a partial VUS is proposed alternatively in this work. This partial VUS is represented as the probability and formulated with the integral equations using two kinds of the ROC surface functions.We derive some relationships among the first type of the ROC surface function, its derivatives and the second partial derivative of the partial VUS. It is found that the optimal thresholds for the ROC surface are derived by using derivatives of the ROC surface function or the third partial derivative of the partial VUS. And the second type ROC surface function is discussed and explained with the results obtained from the first type of the ROC surface function. Various normal distribution functions are illustrated to find two ordered optimal threshold using the partial VUS.
Keywords : Accuracy, classifier, discrimination, sensitivity, specificity.