Multi-class ROC analysis from a multi-objective optimisation perspective

Copyright © 2006 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Pattern Recognition Letters . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition Letters, Vol. 27 Issue 8 (2006), DOI: 10.1016/j.patrec.2005.10.016Notes: Receiver operating characteristics (ROC) are traditionally used for assessing and tuning classifiers discriminating between two classes. This paper is the first to set ROC analysis in a multi-objective optimisation framework and thus generalise ROC curves to any number of classes, showing how multi-objective optimisation may be used to optimise classifier performance. An important new result is that the appropriate measure for assessing overall classifier quality is the Gini coefficient, rather than the volume under the ROC surface as previously thought. The method is currently being exploited in a KTP project with AI Corporation on detecting credit card fraud.The receiver operating characteristic (ROC) has become a standard tool for the analysis and comparison 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 an extension to the standard two-class ROC for multi-class problems. We define the ROC surface for the Q-class problem in terms of a multi-objective optimisation problem in which the goal is to simultaneously minimise the Q(Q − 1) misclassification rates, when the misclassification costs and parameters governing the classifier’s behaviour are unknown. We present an evolutionary algorithm to locate the Pareto front—the optimal trade-off surface between misclassifications of different types. The use of the Pareto optimal surface to compare classifiers is discussed and we present a straightforward multi-class analogue of the Gini coefficient. The performance of the evolutionary algorithm is illustrated on a synthetic three class problem, for both k-nearest neighbour and multi-layer perceptron classifiers

A discussion on the validation tests employed to compare human action recognition methods using the MSR Action3D dataset

This paper aims to determine which is the best human action recognition method based on features extracted from RGB-D devices, such as the Microsoft Kinect. A review of all the papers that make reference to MSR Action3D, the most used dataset that includes depth information acquired from a RGB-D device, has been performed. We found that the validation method used by each work differs from the others. So, a direct comparison among works cannot be made. However, almost all the works present their results comparing them without taking into account this issue. Therefore, we present different rankings according to the methodology used for the validation in orden to clarify the existing confusion.Comment: 16 pages and 7 table