Multi-performance fusion of classification systems

Abstract

Given two legacy exploitation systems, whose performances are known, one might wish to determine if combining these together using some rule would yield a new exploitation system with improved performance. This is the fusion process. Often there are several performance objectives one would consider in this process. We investigate the fusion process based upon multiple performances. This is related to multi-objective optimization, but is different in some aspects. In this paper we pose a multi-performance problem for combining two classifications systems and derive the multi-performance fusion theory. A classification system with M possible output labels will have M(M-1) possible errors. The Receiver Operating Characteristic (ROC) manifold was created to quantify all of these errors. The assumption of independence is usually made to simply the mathematics of combining the individual systems into one system. Boolean rules do not exist for multiple symbols, thus, Boolean-like rules were created that would yield label fusion rules. An M-label system will have M! consistent rules. The formula for the resultant ROC manifold of the fused classification systems which incorporates the individual classification systems previously was derived. For the multi-performance problem we show how the set of permutations of the label set is used to generate all of the consistent rules and how the permutation matrix is incorporated into a single formula for the ROC manifold. Examples will be given that demonstrate how the solution to the multi-performance fusion problem relates to the solution of the single performance fusion problem.