The ROC manifold of fused independent classification systems

A classification system such as an automatic target recognition (ATR) system with N labels (or decisions) will have N(N - 1) possible errors. The receiver operating characteristic (ROC) manifold was created to quantify all of these errors. When multiple ATR systems are fused, the assumption of independence is usually made in order to mathematically combine the individual ROC manifolds for each system into one ROC manifold. This paper will investigate label fusion (also called decision fusion) of multiple classification systems that have the same number of output labels. The formula for the resultant ROC manifold of the fused classification systems which incorporates the individual classification systems will be derived. Specifically, given a fusion rule and two classification systems, the ROC manifold for the fused system is produced. We generate a formulas for the Boolean-like AND rule and give the resultant ROC manifold for the fused system. An example is given that demonstrates how this formula is used.