The meaning and use of the volume under a three-class ROC surface (VUS)
The meaning and use of the volume under a three-class ROC surface (VUS)
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DOI：
10.1109/tmi.2007.908687
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发表时间：
2008-05-01
影响因子：
10.6
通讯作者：
Frey, Eric. C.
中科院分区：
文献类型：
--
作者：
He, Xin;Frey, Eric. C.
在此之前，我们提出了一种基于决策理论的三类受试者工作特征（ROC）分析方法。在该方法中，三类ROC曲面（VUS）下的体积作为品质因数（FOM）并测量三类任务性能。根据多个决策准则，在决策理论下证明了所提出的三类ROC分析方法是最优的。在数据线性条件满足的前提下，提出了一种最优的三类线性观测器，使每一类的检验统计量之间的信噪比（SNR）同时达到最大.这种三类ROC分析方法的适用性将进一步增强的发展的直观意义的VUS和一个更一般的方法来计算VUS，提供了一个估计其标准误差。在本文中，我们调查的一般意义和使用VUS作为FOM的三类分类任务的性能。我们表明，VUS值，这是从一个评级过程中获得的，等于百分比正确的连续评级数据在相应的分类程序。这种关系的意义不仅仅是为三类ROC分析提供另一个理论基础-它使VUS值的统计分析成为可能。基于这种关系，我们开发并测试了计算VUS及其方差的算法。最后，我们回顾了目前提出的三类ROC分析方法的现状，并得出结论，它扩展和统一的决策理论，线性判别分析和心理物理基础的二进制ROC分析在三个类的范例。
Previously, we have proposed a method for three-class receiver operating characteristic (ROC) analysis based on decision theory. In this method, the volume under a three-class ROC surface (VUS) serves as a figure-of-merit (FOM) and measures three-class task performance. The proposed three-class ROC analysis method was demonstrated to be optimal under decision theory according to several decision criteria. Further, an optimal three-class linear observer was proposed to simultaneously maximize the signal-to-noise ratio (SNR) between the test statistics of each pair of the classes provided certain data linearity condition. Applicability of this three-class ROC analysis method would be further enhanced by the development of an intuitive meaning of the VUS and a more general method to calculate the VUS that provides an estimate of its standard error. In this paper, we investigated the general meaning and usage of VUS as a FOM for three-class classification task performance. We showed that the VUS value, which is obtained from a rating procedure, equals the percent correct in a corresponding categorization procedure for continuous rating data. The significance of this relationship goes beyond providing another theoretical basis for three-class ROC analysis-it enables statistical analysis of the VUS value. Based on this relationship, we developed and tested algorithms for calculating the VUS and its variance. Finally, we reviewed the current status of the proposed three-class ROC analysis methodology, and concluded that it extends and unifies decision theoretic, linear discriminant analysis, and psychophysical foundations of binary ROC analysis in a three-class paradigm.