Receiver Operating Characteristic, also known as the ROC curve.

Receiver Operating Characteristic curve, also known as an ROC curve, is a graphical plot comparing the true positive rates and the false positive rates of a classifier as the discrimination threshold of the classifier is varied.

The true positive rate, defined as is the the fraction of true positives out of the positives, is also called the sensitivity or recall. The false positive rate, defined as the fraction of false positives out of the negatives, is equivalent to 1 - sensitivity

In its original form, the ROC curve was used to summarize performance of a binary classification task, although it can be extended for use in multi-class problems.

A classifier performing at chance is expected to have true positive and false positive rates that are equal, producing a diagonal line. Classifiers that exceed chance produce a curve above this diagonal. The area under the curve (or AUC) is commonly used as a summary of the ROC curve and as a measure of classifier performance. The AUC is equal to the probability that a classifier will rank a randomly chosen positive case higher than a randomly chosen negative one. This is equivalent to the Wilcoxon test of ranks.

ROC curves enable visualizing and organizing classifier performance without regard to class distributions or error costs. This can be helpful when investigating learning with skewed distributions or cost-sensitive learning.

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