If you look at the f1_score function in sklearn.metrics, you will see an ‘average’ argument. This argument defaults to ‘binary’. However, when dealing with multi-class classification, you can’t use average = ‘binary’. You can choose one of ‘micro’, ‘macro’, or ‘weighted’ for such a case (you can also use None; you will get f1_scores for each label in this case, and not a single value).
When you set average = ‘macro’, you calculate the f1_score of each label and compute a simple average of these f1_scores to arrive at the final number.
By setting average = ‘weighted’, you calculate the f1_score for each label, and then compute a weighted average (weights being proportional to the number of items belonging to that label in the actual data).
When you set average = ‘micro’, the f1_score is computed globally. Total true positives, false negatives, and false positives are counted. Essentially, global precision and recall are considered.
This can be understood with an example. Consider:
y_true = [0,0,0,1,1,1,2,2,2,2] y_pred = [1,0,0,1,1,0,2,2,1,2]
Now, let’s first compute the f1_scores for the individual labels:
from sklearn.metrics import f1_score f1_score(y_true, y_pred, average = None) >> array([0.66666667, 0.57142857, 0.85714286])
Now, the macro score, a simple average of the above numbers, should be 0.698.
f1_score(y_true, y_pred, average = 'macro') >> 0.6984126984126985
The weighted average has weights equal to the number of items of each label in the actual data. So, it should equal (0.6667*3+0.5714*3+0.857*4)/10 = 0.714
f1_score(y_true, y_pred, average = 'weighted') >> 0.7142857142857142
For the micro average, let’s first calculate the global recall. Out of all the labels in y_true, 7 are correctly predicted in y_pred. This brings the recall to 0.7. Next, let us calculate the global precision. Out of all the labels in y_pred, 7 have correct labels. This brings the precision to 0.7. Thus, micro f1_score will be 2*0.7*0.7/(0.7+0.7) = 0.7
f1_score(y_true, y_pred, average = 'micro') >> 0.7
You can try this for any other y_true and y_pred arrays. The global precision and global recall are always the same. Therefore, calculating the micro f1_score is equivalent to calculating the global precision or the global recall.
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Thank you for the crystal-clear explanation!