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This paper presents a method to quantify detection system families (DSFs) based upon the Precision-Recall (PR) curve and variations of the PR curve. The PR curve is related to the Receiver Operating Characteristic (ROC) curve. The ROC curve of a detection system family shows the trade-off between the probabilities of a true positive classification versus the probability of a false positive classification. The conditional probabilities are conditioned on the true outcomes. The PR curve is similar in the sense that the conditional probabilities are conditioned on the outcomes of the detection systems that "say" they are true outcomes. We present the function that produces the PR curve, called the PR function. We produce the (nonlinear) transformation that relates the ROC function to the Precision-Recall function. We discuss variations of the Precision-Recall function that will be useful.
Given two detection system families A and B, for which we know their respective ROC functions, we know the transformation that produces the ROC function of the conjunction of A with B, and the ROC function of the disjunction of A with B. We review these transformations and relate them to the PR functions. In particular, given the PR functions for detection system families A and B, we produce the PR functions for the detection system families A conjoin B and A disjoin B. Examples are given that demonstrate the theory and usefulness of the transformation to predict the performance of the fused systems. The extension to multiple label classification systems will be presented.
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