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F1-score is the harmonic mean of precision and recall. The y-axis of recall is true positive rate (which is also recall). So, sometime classifiers can have low recall but very high AUC, what that means?

What are the differences between AUC and F1-score?

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    $\begingroup$ AUC is unclear if you don't specify the curve. Do you mean area under the ROC curve, area under the PR curve, ...? $\endgroup$
    – Marc Claesen
    Commented Nov 7, 2014 at 8:57
  • $\begingroup$ Area under the curve. $\endgroup$
    – RockTheStar
    Commented Nov 7, 2014 at 19:16
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    $\begingroup$ Which curve? ROC? PR? Lift? $\endgroup$
    – Marc Claesen
    Commented Nov 8, 2014 at 10:07
  • $\begingroup$ ROC curve. And the F1-score obtained from that. $\endgroup$
    – RockTheStar
    Commented Nov 9, 2014 at 3:23

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F1 score is applicable for any particular point of the ROC curve. This point may represent for example a particular threshold value in a binary classifier and thus corresponds to a particular value of precision and recall.

Remember, F score is a smart way to represent both recall and precision. For F score to be high, both precision and recall should be high.

Thus, the ROC curve is for various different levels of thresholds and has many F score values for various points on its curve.

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    $\begingroup$ Interesting aspect. But as far as I understand, F1 score is based on Recall and Precision, whereas AUC/ROC consists of Recall and Specificity. It seems that they are not the same thing. I agree with F score is a point, and ROC is a set of points with different threshold, but I dont think they are the same 'cause of different definition. Can you help me to make it clearer. Thanks $\endgroup$
    – Catbuilts
    Commented Oct 12, 2018 at 6:42
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AUC is of dimension [PRECISION]*[RECALL] and it is the area under ROC curve. F1 is for a fixed pair of precision and recall. So they are different. But there are some connections. See this: http://pages.cs.wisc.edu/~jdavis/davisgoadrichcamera2.pdf

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The axes of an ROC curve are the true positive rate (recall, AKA sensitivity) and false positive rate (false alarm rate), not precision, AKA PPV, positive predictive value.

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