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Table 4 Recap of the relationship between the multi-category metrics and the basic rates of the confusion matrix

From: The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation

Scenario Basic rates condition # guaranteed high basic rates
high MCC means: high TPR, TNR, PPV, and NPV 4
high BA means: high TPR, TNR, and at least one of PPV and NPV 3
high BM means: high TPR, TNR, and at least one of PPV and NPV 3
high MK means: high PPV, NPV, and at least one of TPR and TNR 3
high F1 score means: high PPV and TPR 2
high accuracy means: high TPR and PPV, or high TNR and NPV 2
  1. #: integer number. MCC: Matthews correlation coefficient (Eq. 5). BA: balanced accuracy (Eq. 6). BM: bookmaker informedness (Eq. 7). MK: markedness (Eq. 8). F1 score: harmonic mean of TPR and PPV (Supplementary information). Accuracy: ratio between correctly predicted data instances and all data instances (Supplementary information). We call “basic rates” these four indicators: TPR, TNR, PPV, and NPV