Receiver operating characteristic (ROC) curve

Given a binary classifier, a receiver operating characteristic curve plots the true positive rate against the false positive rate (aka type I error) as a function of the classifier’s threshold.

In such a plot, the diagonal represents a random classifier. Any curve above the diagonal represents better-than-chance performance, and any classifier below the diagonal represents a worse-than-chance performance. (In this case, taking the complement of the original classifier would give a better-than-chance performance.) A perfect classifier exists at the point .

The area under the ROC curve represents an aggregate measure of a classifier’s performance across all possible threshold values:

• A classifier that is always right (“perfect classifier”) has area 1.0;
• A random classifier has area 0.5; and
• A classifier that is always wrong has area 0.0.

Application to multi-class evaluation

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