Volume under the ROC Surface for Multi-class Problems
نویسندگان
چکیده
Receiver Operating Characteristic (ROC) analysis has been successfully applied to classifier problems with two classes. The Area Under the ROC Curve (AUC) has been elected as a better way to evaluate classifiers than predictive accuracy or error and has also recently used for evaluating probability estimators. However, the extension of the Area Under the ROC Curve for more than two classes has not been addressed to date, because of the complexity and elusiveness of its precise definition. Some approximations to the real AUC are used without an exact appraisal of their quality. In this paper, we present the real extension to the Area Under the ROC Curve in the form of the Volume Under the ROC Surface (VUS), showing how to compute the polytope that corresponds to the absence of classifiers (given only by the trivial classifiers), to the best classifier and to whatever set of classifiers. We compare the real VUS with “approximations” or “extensions” of the AUC for more than two classes.
منابع مشابه
Developments in Roc Surface Analysis and Assessment of Diagnostic Markers in Three-class Classification Problems
• This article reviews current state of the art of ROC surface analysis and illustrates its use through an application on a pancreatic cancer diagnostic marker. Receiver Operating Characteristic (ROC) surfaces have been studied in the literature essentially only during the last decade and are considered as a natural generalization of ROC curves in three-class diagnostic problems. This article p...
متن کاملRanking Multi-Class Data: Optimality and Pairwise Aggregation
It is the primary purpose of this paper to set the goals of ranking in a multiple-class context rigorously, following in the footsteps of recent results in the bipartite framework. Under specific likelihood ratio monotonicity conditions, optimal solutions for this global learning problem are described in the ordinal situation, i.e. when there exists a natural order on the set of labels. Criteri...
متن کاملROCS: Receiver Operating Characteristic Surface for Class-Skewed High-Throughput Data
The receiver operating characteristic (ROC) curve is an important tool to gauge the performance of classifiers. In certain situations of high-throughput data analysis, the data is heavily class-skewed, i.e. most features tested belong to the true negative class. In such cases, only a small portion of the ROC curve is relevant in practical terms, rendering the ROC curve and its area under the cu...
متن کاملMulti-class ROC analysis from a multi-objective optimisation perspective
The Receiver Operating Characteristic (ROC) has become a standard tool for the analysis and comparision of classifiers when the costs of misclassification are unknown. There has been relatively little work, however, examining ROC for more than two classes. Here we discuss and present a number of different extensions to the standard two-class ROC for multi-class problems. We define the ROC surfa...
متن کاملAdaptive Consensus Control for a Class of Non-affine MIMO Strict-Feedback Multi-Agent Systems with Time Delay
In this paper, the design of a distributed adaptive controller for a class of unknown non-affine MIMO strict-feedback multi agent systems with time delay has been performed under a directed graph. The controller design is based on dynamic surface control method. In the design process, radial basis function neural networks (RBFNNs) were employed to approximate the unknown nonlinear functions. S...
متن کامل