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Harmonic means of F1 Score

Recall = TP / (TP + FN)

Precision = TP / (TP + FP)


SOLVE

F1 Score = Recall * Precision /  (Recall + Precision)

F1 = (TP / (TP + FN) * TP / (TP + FP))  / ( TP / (TP + FN) + TP / (TP +FP) )

F1 = ( TP^2 / (TP + FP) + (FP + FN)  )  / (TP (TP + FN) / (TP + FP) (TP + FN))  + (TP (TP + FP) / (TP + FP) (TP + FN) )

F1 =  TP^2 / (2 TP^2 + FNTP + FPTP)

F1 =  TP^2 / (TP^2 ( TP^2 + FN / TP + FP / TP))

F1 =  1 / (TP^2 + FN / TP + FP / TP)


Thus,  F1 Score is a harmonic mean.


  

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