Solved – Recall and AUC of a binary classifier

aucdata miningroc

Is it possible for a binary classifier to have a recall of 0.0 for one of the classes and
at the same time an area under the ROC curve (AUC) of 1.0 for the same class?

Best Answer

ROC curves are false negative rate vs true positive rate graph. If you have AUC = 1, by definition you have perfect classifier.

From Information retrieval viewpoint ; if you have AUC = 1 then you have perfect recall and perfect precision. You recall all documents which exists about this topic, also all the documents you recall are relevant to your topic.

I would like to add more information for response to commenter.

Following is a graph from "ROC Graphs: Notes and Practical Considerations for Data Mining Researchers, Tom Fawcett"

Figure 2 of ROC Graphs

A discrete classifier is one that outputs only a class label. 
Each discrete classifier produces an (FP rate,TP rate) pair, 
which corresponds to a single point in ROC space. 
...
The point (0;1) represents perfect classification. 
D's performance is perfect as shown.
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