Why is the F-measure usually used for (supervised) classification tasks, whereas the G-measure (or Fowlkes–Mallows index) is generally used for (unsupervised) clustering tasks?

The F-measure is the harmonic mean of the precision and recall.

The G-measure (or Fowlkes–Mallows index) is the geometric mean of the precision and recall.

Below is a plot of the different means.

enter image description here

F1 (harmonic) $= 2\cdot\frac{precision\cdot recall}{precision + recall}$

Geometric $= \sqrt{precision\cdot recall}$

Arithmetic $= \frac{precision + recall}{2}$

The reason I ask is that I need to decide which average to use in a NLG task, where I measured BLEU and ROUGE ( where BLEU is equivalent to precision and ROUGE to recall). How should I calculate the mean of these scores?

  • $\begingroup$ Maybe it's just how the defination goes! $\endgroup$ – Aditya Aug 12 '18 at 9:42
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    $\begingroup$ @Aditya, you are right, it was just a badly formulated questions about definition. I edited it reformulating into something more concrete. $\endgroup$ – BrunoGL Aug 12 '18 at 9:57

The Fı-score is preferred to simple classification accuracy in order to counter the problem of imbalanced datasets; if the thing you are looking for occurs only rarely anyway then a naive classifier can always say no and appear to be working very well! A variant on Fı is Fß, where

Fß = (1+ß²) × [ (P × R) ÷ ( (ß² × P) + R ) ]

Vary ß to balance precision and recall. As to the why F or G, I believe it to be empirical - you don't say if you are classifying or clustering in your own application?

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    $\begingroup$ Thanks for the answer, but I think you miss understood my question. I don't mean to compare F1 vs. simple accuracy., instead, I mean to compare the Harmonic vs Geometric vs Arithmetic means. I am not doing traditional classification or clustering, I have a NLG task, which is measured in BLEU and ROUGE which could be averaged with one of the means, but I am not sure which to pick. $\endgroup$ – BrunoGL Aug 12 '18 at 14:56

If Precision and Recall are similar, F1 is a good single measure to compare different models.

Short and sweet :)

  • $\begingroup$ I don't see how you even attempted to answer my question... $\endgroup$ – BrunoGL Feb 23 '19 at 18:22

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