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Averaging Methods#

For multiclass workflows like classification or object detection, metrics such as precision, recall, and F1-score are computed per class. To compute a single value that represents model performance across all classes, these per-class scores need to be aggregated. There are a few different averaging methods for doing this, most notably:

  • Macro: unweighted mean of all per-class scores
  • Micro: global average of per-sample TP, FP, FN scores
  • Weighted: mean of all per-class scores, weighted by sample sizes for each class

Example: Multiclass Classification#

Let’s consider the following multiclass classification metrics, computed across a total of 10 samples:

Class # Samples # True Positives # False Positives # False Negatives Precision Recall F1-score
Airplane 3 2 1 1 0.67 0.67 0.67
Boat 1 1 3 0 0.25 1.0 0.4
Car 6 3 0 3 1.0 0.5 0.67
Total 10 6 4 4 - - -

Macro Average#

Macro average is perhaps the most straightforward among the numerous options and is computed by taking an unweighted mean of all the per-class scores:

\[ \begin{align} \text{F}_{1 \, \text{macro}} &= \frac{\text{F}_{1 \, \texttt{Airplane}} + \text{F}_{1 \, \texttt{Boat}} + \text{F}_{1 \, \texttt{Car}}}{3} \\[1em] &= \frac{0.67 + 0.4 + 0.67}{3} \\[1em] &= 0.58 \end{align} \]

Micro Average#

In contrast to macro, micro average computes a global average by counting the sums of true positive (TP), false negative (FN) and false positive (FP).

Micro precision and micro recall are computed with the standard precision and recall formulas, using the total TP/FP/FN counts across all classes:

\[ \begin{align} \text{Precision}_\text{micro} &= \frac{\text{TP}_\text{Total}}{\text{TP}_\text{Total} + \text{FP}_\text{Total}} \\[1em] &= \frac{6}{6 + 4} \\[1em] &= 0.6 \end{align} \]
\[ \begin{align} \text{Recall}_\text{micro} &= \frac{\text{TP}_\text{Total}}{\text{TP}_\text{Total} + \text{FN}_\text{Total}} \\[1em] &= \frac{6}{6 + 4} \\[1em] &= 0.6 \end{align} \]

What about micro F1? Plug the micro-averaged values for precision and recall into the standard formula for F1-score:

\[ \begin{align} \text{F}_{1 \, \text{micro}} &= 2 \times \frac{\text{Precision}_\text{micro} \times \text{Recall}_\text{micro}}{\text{Precision}_\text{micro} + \text{Recall}_\text{micro}} \\[1em] &= 2 \times \frac{0.6 \times 0.6}{0.6 + 0.6} \\[1em] &= 0.6 \end{align} \]

Note that precision, recall, and F1-score all have the same value: \(0.6\). This is because micro-averaging essentially computes the proportion of correctly classified instances out of all instances, which is the definition of overall accuracy.

In the multiclass classification cases where each sample has a single label, we get the following:

\[ \text{F}_{1 \, \text{micro}} = \text{Precision}_\text{micro} = \text{Recall}_\text{micro} = \text{Accuracy} \]

Weighted Average#

Weighted average computes the mean of all per-class scores while considering each class’s support. In this case, support is the number of actual instances of the class in the dataset.

For example, if there are 3 samples of class Airplane, then the support value of class Airplane is 3. In other words, support is the sum of true positive (TP) and false negative (FN) counts. The weight is the proportion of each class’s support relative to the sum of all support values:

\[ \begin{align} \text{F}_{1 \, \text{weighted}} &= \left( \text{F}_{1 \, \texttt{Airplane}} \times \tfrac{\text{#}\ \texttt{Airplane}}{\text{# Total}} \right) + \left( \text{F}_{1 \, \texttt{Boat}} \times \tfrac{\text{#}\ \texttt{Boat}}{\text{# Total}} \right) + \left( \text{F}_{1 \, \texttt{Car}} \times \tfrac{\text{#}\ \texttt{Car}}{\text{# Total}} \right) \\[1em] &= \left( 0.67 \times \tfrac{3}{10} \right) + \left( 0.4 \times \tfrac{1}{10} \right) + \left( 0.67 \times \tfrac{6}{10} \right) \\[1em] &= 0.64 \end{align} \]

Which Method Should I Use?#

You would generally use these three methods to aggregate the metrics computed per class. Averaging is most commonly used in multiclass/multi-label classification and object detection tasks.

So which average should you use?

If you’re looking for an easily understandable metric for overall model performance regardless of class, micro average is probably best.

If you want to treat all classes equally, then using macro average would be a good choice.

If you have an imbalanced dataset but want to assign more weight to classes with more samples, consider using weighted average instead of macro average.