Micro Recall

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

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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.

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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.

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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.

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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.

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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.