F. Roli and S. Vitulano (Eds.): ICIAP 2005, LNCS 3617, pp. 778 – 785, 2005. © Springer-Verlag Berlin Heidelberg 2005 Estimating the ROC Curve of Linearly Combined Dichotomizers Claudio Marrocco, Mario Molinara, and Francesco Tortorella Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell’Informazione e Matematica Industriale, Università degli Studi di Cassino, 03043 Cassino (FR), Italy {c.marrocco, m.molinara, tortorella}@unicas.it Abstract. A well established technique to improve the classification perform- ances is to combine more classifiers. In the binary case, an effective instrument to analyze the dichotomizers under different class and cost distributions provid- ing a description of their performances at different operating points is the Re- ceiver Operating Characteristic (ROC) curve. To generate a ROC curve, the outputs of the dichotomizers have to be processed. An alternative way that makes this analysis more tractable with mathematical tools is to use a paramet- ric model and, in particular, the binormal model that gives a good approxima- tion to many empirical ROC curves. Starting from this model, we propose a method to estimate the ROC curve of the linear combination of two dichoto- mizers given the ROC curves of the single classifiers. A possible application of this approach has been successfully tested on real data set. 1 Introduction Dichotomizers (i.e. two-class classifiers) are used in many critical applications (e.g., automated diagnosis, fraud detection, currency verification) which require highly discriminating classifiers. In order to improve the classification performance a well established technique is to combine more classifiers so as to take advantage of the strengths of the single classifiers and avoid their weaknesses. To this aim, a huge number of possible combination rules have been proposed up to now which generally try to decrease the classification error. However, the applications considered fre- quently involve cost matrices and class distributions both strongly asymmetric and dynamic and in such cases the overall error rate, usually employed as a reference performance measure in classification problems, is not a suitable metric for evaluating the quality of the classifier [1]. A more effective tool for correctly quantifying the accuracy and analyzing the di- chotomizer under different class and cost distributions is given by the Receiver Oper- ating Characteristic (ROC) curve. It provides a description of the performance of the dichotomizer at different operating points, which is independent of the prior prob- abilities of the two classes. ROC analysis is based in statistical decision theory and was first employed in signal detection problems [2]; it is now common in medical diagnosis and particularly in medical imaging [3]. In the Pattern Recognition field, ROC analysis is increasingly adopted for many central issues such as the evaluation