Optimal Linear Combination of Dichotomizers via AUC

A well established technique to improve the classification performances is to combine more classifiers. However, the possible combination rules proposed up to now generally try to decrease the classification error rate, which is a performance measure not suitable in many real situations and particularly when dealing with two class problems. In this case, an effective instrument to analyze the dichotomizers under different class and cost distributions is the Receiver Operating Characteristic (ROC) curve. In particular, a good performance measure is given by the Area under the Receiver Operating Characteristic curve (AUC), whose effectiveness in measuring the classification quality has been proved in many recent papers. In this paper we consider the linear combination of two dichotomizers since it is the most frequently adopted combination rule and propose a method to achieve the optimal weight of the combination based on the maximization of the AUC of the resulting classification system. The effectiveness of the approach has been confirmed by the tests performed on standard datasets.