Learning Classification Systems Maximizing the Area under the Roc Curve

Permission is herewith granted to Università degli Studi di Cassino to circulate and to have copied for non-commercial purposes, at its discretion, the above title upon the request of individuals or institutions. Acknowledgements This work would not have been possible without the support I received from many people. A big thank you to all who have helped me in some way or other to complete this thesis. The most important person I would like to thank is my supervisor: Francesco Tor-torella. In these three years he has guided me through this work. Having him as supervisor is a continuous source of motivation and gives you the feeling that you can do something useful. He is always ready to give you advice when you need, encouraging you to pursue your individual interest. I learnt a lot from our discussions on ROC curve and life. Thanks! I would also like to thank prof. Bob Duin of the TU Delft. In Netherlands, I spent five beautiful months and his help was important to complete this thesis. Then, my special thanks to all members of the LIT group, who ensured that it was always funny working there. Thanks for all the support during our " numerous " coffee breaks of everyday! They are friends more than colleagues. Finally, my family, what would I have been without them? Thanks for everything. vii Summary This thesis is concerned with supervised classification problems in which the aim is to build a rule to assign objects to one of a finite set of classes. Systems able to perform these operations using a set of known examples are called classifiers. In particular, this work focuses on problems where we have to distinguish between two mutually exclusive classes. In this case, many distinct criteria for comparing performance of rules can be used. In this thesis an analysis of the Receiver Operating Characteristics (ROC) curve methodology in pattern recognition is performed and the use of the Area under the ROC curve (AUC) as performance measure for building dichotomizers and combination rules is proposed. The thesis is organized as follows: • Chapter 1: we introduce the framework of pattern recognition in which this work is placed. Starting from the basis of statistical pattern recognition we introduce the main problems of the topics of this thesis that are the two-class classification and in this context the combination of classifiers. • Chapter 2: the …