Receiver Operating Characteristic Curve (ROC)

A graph of true positive rate versus false positive rate for different classification thresholds in binary classification. The shape of an ROC curve suggests a binary classification model's ability to separate positive classes from negative classes. Suppose, for example, that a binary classification model perfectly separates all the negative classes from all the positive classes: !A number line with 8 positive examples on the right side and 7 negative examples on the left. The ROC curve for the preceding model looks as follows: !An ROC curve. The x-axis is False Positive Rate and the y-axis is True Positive Rate. The curve has an inverted L shape. The curve starts at (0.0,0.0) and goes straight up to (0.0,1.0). Then the curve goes from (0.0,1.0) to (1.0,1.0). In contrast, the following illustration graphs the raw logistic regression values for a terrible model that can't separate negative classes from positive classes at all: !A number line with positive examples and negative classes completely intermixed. The ROC curve for this model looks as follows: !An ROC curve, which is actually a straight line from (0.0,0.0) to (1.0,1.0). Meanwhile, back in the real world, most binary classification models separate positive and negative classes to some degree, but usually not perfectly. So, a typical ROC curve falls somewhere between the two extremes: !An ROC curve. The x-axis is False Positive Rate and the y-axis is True Positive Rate. The ROC curve approximates a shaky arc traversing the compass points from West to North. The point on an ROC curve closest to (0.0,1.0) theoretically identifies the ideal classification threshold. However, several other real-world issues influence the selection of the ideal classification threshold. For example, perhaps false negatives cause far more pain than false positives. A numerical metric called AUC summarizes the ROC curve into a single floating-point value.