Micro- and Macro-average of Precision, Recall and F-Score

I posted several articles explaining how precision and recall can be calculated, where F-Score is the equally weighted harmonic mean of them. I was wondering- how to calculate the average precision, recall and harmonic mean of them of a system if the system is applied to several sets of data.

Tricky, but I found this very interesting. There are two methods by which you can get such average statistic of information retrieval and classification.

1. Micro-average Method

In Micro-average method, you sum up the individual true positives, false positives, and false negatives of the system for different sets and the apply them to get the statistics. For example, for a set of data, the system's

True positive (TP1)= 12
False positive (FP1)=9
False negative (FN1)=3

Then precision (P1) and recall (R1) will be 57.14 and 80

and for a different set of data, the system's


True positive (TP2)= 50
False positive (FP2)=23
False negative (FN2)=9

Then precision (P2) and recall (R2) will be 68.49 and 84.75

Now, the average precision and recall of the system using the Micro-average method is

Micro-average of precision = (TP1+TP2)/(TP1+TP2+FP1+FP2) = (12+50)/(12+50+9+23) = 65.96
Micro-average of recall = (TP1+TP2)/(TP1+TP2+FN1+FN2) = (12+50)/(12+50+3+9) = 83.78

The Micro-average F-Score will be simply the harmonic mean of these two figures.

2. Macro-average Method

The method is straight forward. Just take the average of the precision and recall of the system on different sets. For example, the macro-average precision and recall of the system for the given example is

Macro-average precision = (P1+P2)/2 = (57.14+68.49)/2 = 62.82
Macro-average recall = (R1+R2)/2 = (80+84.75)/2 = 82.25

The Macro-average F-Score will be simply the harmonic mean of these two figures.

Suitability
Macro-average method can be used when you want to know how the system performs overall across the sets of data. You should not come up with any specific decision with this average.

On the other hand, micro-average can be a useful measure when your dataset varies in size.