Micro F1 Score

Micro F1 Score

The Micro F1 Score is an evaluation metric used primarily in multi-class and multi-label classification tasks. Unlike Macro F1 Score, it calculates global counts of true positives, false positives, and false negatives across all classes, then uses these to compute a single Precision, Recall, and F1 Score.

It is most useful when the dataset is imbalanced and you care more about overall performance than per-class fairness.

Definition

$\text{Micro F1}=2\cdot \frac{\text{Micro Precision}\cdot \text{Micro Recall}}{\text{Micro Precision}+\text{Micro Recall}}$

Where:

$\text{Micro Precision}=\frac{\sum TP}{\sum TP+\sum FP}$

$\text{Micro Recall}=\frac{\sum TP}{\sum TP+\sum FN}$

Instead of averaging individual class scores, Micro F1 aggregates global totals of:

• True Positives (TP)
• False Positives (FP)
• False Negatives (FN)

Step-by-Step Example

Suppose a 3-class classification problem with:

• Class A: TP=50, FP=10, FN=5
• Class B: TP=30, FP=15, FN=10
• Class C: TP=20, FP=5, FN=15

Global totals:

• TP = 50 + 30 + 20 = 100
• FP = 10 + 15 + 5 = 30
• FN = 5 + 10 + 15 = 30

$\text{Micro Precision}=\frac{100}{100+30}=\frac{100}{130}\approx 0.769$

$\text{Micro Recall}=\frac{100}{100+30}=\frac{100}{130}\approx 0.769$

$\text{Micro F1}=2\cdot \frac{0.769\cdot 0.769}{0.769+0.769}=0.769$

Micro Precision and Recall are equal, so Micro F1 equals them.

Micro vs Macro vs Weighted F1

Metric	How It Works	Best For
Micro F1	Global average across all classes (TP, FP, FN summed first)	Imbalanced data where you care about overall performance
Macro F1	Average of F1 scores per class (unweighted)	Equal importance for each class
Weighted F1	Average of F1 scores per class (weighted by class size)	Imbalanced data, focus on majority classes

Use Cases

• Multi-label text classification
• Image tagging tasks
• Medical diagnosis systems with multiple labels
• Imbalanced datasets with focus on global accuracy

Limitations

• May **hide poor performance** on minority classes
• Doesn't reflect per-class fairness

Related Pages

• F1 Score
• Macro F1
• Weighted F1
• Precision
• Recall
• Accuracy
• Confusion Matrix

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