1. Recall Recap (Binary Case)

  • Recall = Of all actual positives, how many did the model correctly identify?

$Recall = \frac{TP}{TP + FN}$

Where:

  • TP = True Positives
  • FN = False Negatives

2. Multiclass Extension

For K classes, recall can be extended in macro and micro styles:

  • Macro Recall: Compute recall per class (OvR), then average equally.
  • Micro Recall: Pool all classes together, then compute recall once.

3. Definition of Micro Recall

$Recall_{micro} = \frac{\sum_{i=1}^{K} TP_i}{\sum_{i=1}^{K} (TP_i + FN_i)}$

  • Aggregate true positives and false negatives across all classes.
  • Then compute recall as if it’s one big binary classification: correct vs incorrect.

4. Key Characteristics

  • Micro Recall = Micro Precision = Micro F1 in multiclass settings.
    • This happens because when you pool everything, the denominators line up (all predictions vs all ground truth).
  • Strongly influenced by majority classes, since their TP and FN dominate the totals.
  • Good when you care about overall system accuracy and not fairness across classes.

5. Example

Suppose we have 3 classes (A, B, C):

  • Class A: TP = 40, FN = 10
  • Class B: TP = 30, FN = 20
  • Class C: TP = 10, FN = 30

Macro Recall:

  • Recall(A) = 40 / (40+10) = 0.80
  • Recall(B) = 30 / (30+20) = 0.60
  • Recall(C) = 10 / (10+30) = 0.25
  • Macro Recall = (0.80 + 0.60 + 0.25) / 3 = 0.55

Micro Recall:

$\frac{40+30+10}{(40+10)+(30+20)+(10+30)} = \frac{80}{140} \approx 0.571$

So Micro Recall (0.571) is a global measure, while Macro Recall (0.55) gives equal weight to all classes.

Summary

  • Micro Recall = global recall across all classes.
  • Counts TP and FN across classes before computing.
  • Favors majority classes.
  • Often reported with Macro Recall to show both overall and per-class fairness.