A mathematical framework for the optimization of rejection and ROC thresholds in the fusion of correlated sensor data
Trevor I. Laine, Kenneth W. Bauer · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2004
In pattern recognition applications, significant costs can be associated with various decision options and a minimum acceptable level of confidence is often required. Combat target identification is one example where the incorrect labeling of Targets and Non-targets incurs substantial costs; yet, these costs may be difficult to quantify. One way to increase decision confidence is through fusion of data from multiple sources or from multiple looks through time. Numerous methods have been published to determine optimal rules for the fusion of decision labels or to determine the Bayes’ optimal decision if prior and posterior probabilities along with decision costs can be accurately estimated. This paper introduces a mathematical framework to optimize multiple decision thresholds subject to a decision maker’s preferences, when a continuous measure of class membership is available. Decision variables may include rejection thresholds to specify non-declaration regions and ROC thresholds to explore viable true positive and false positive Target classification rates, where the feasible space can be partially visualized by a 3D ROC surface. This methodology yields an optimal class declaration rule subject to decision maker preferences without using explicit costs associated with each type of decision. Some properties of this optimization framework are shown for Gaussian distributions representing Target and Non-target classes with various prior probabilities and correlation levels between simulated multiple sensor looks.