Confidence of a ROC manifold

Abstract

A Classification system such as an Automatic Target Recognition (ATR) 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. Finite truth data will produce an approximation to a ROC manifold. How well does the approximate ROC manifold approximate the TRUE ROC manifold? Several metrics exist that quantify the approximation ability, but researchers really wish to quantify the confidence in the approximate ROC manifold. This paper will review different confidence definitions for ROC curves and will derive an expression for confidence of a ROC manifold. The foundation of the confidence expression is based upon the Chebychev inequality..