Label fusion of classification systems via their ROC functions

Abstract

A classification system with N possible output 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 classication 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 the label fusion (also called decision fusion) of multiple classication systems that have the same number of output labels. Boolean rules do not exist for multiple symbols, thus, we will derive possible Boolean-like rules as well as other rules that will yield label fusion rules. The formula for the resultant ROC manifold of the fused classication systems which incorporates the individual classication systems will be derived. Specically, given a label rule and two classication systems, the ROC manifold for the fused system is produced. We generate formulas for other non-Boolean-like OR and non-Boolean-like AND rules and give the resultant ROC manifold for the fused system. Examples will be given that demonstrate how each formula is used.