A comparison of ROC curves for label-fused within and across classifier systems

When presented with a finite collection of classifiers one might wish to combine the classifiers in hopes that the fused classifier system will perform better than any individual system. The performance of this fused classifier system can be evaluated via the receiver operating characteristic (ROC) curve. The ROC curve depicts the trade off between the probability of true and false positives for a set of parameters on which the classifiers depends. Two considerations when creating the fused classifier system are the types of targets to be identified and the type of fusion to be used. Each of these systems may draw from events which contain either single target types or multiple target types. Thus, the fused classifier system can be characterized as fusing within (single) target type, fusing across (multiple) target types, or a combination of both. There are several ways in which to fuse the classifier systems. One such method is to fuse their resultant labels, i.e., label fusion. In this paper we rigorously define within and across fusion and compare the performance of several label-fused classifier systems. Given the ROC curves for each classifier system and a decision rule, we derive the formula of the ROC curve for the label-fused classifier system for events containing within and across target types. Examples comparing the performance of these fused systems using logical AND and OR, and the majority vote decision rules are given.