When dealing with multi-class classification problems, precision and recall can be extended to handle multiple classes. However, the way you compute these metrics needs to take into account how to aggregate them across different classes. Here are some common methods for averaging precision and recall in a multi-class setting:
Micro-Averaging
Micro-averaging computes the metrics globally by counting the total true positives, false negatives, and false positives.
- Precision (micro): (\frac{\sum_{i} TP_i}{\sum_{i}(TP_i + FP_i)})
- Recall (micro): (\frac{\sum_{i} TP_i}{\sum_{i}(TP_i + FN_i)})
Macro-Averaging
Macro-averaging computes the metrics for each class and then takes the average.
- Precision (macro): (\frac{1}{C}\sum_{i=0}^{C-1} P(i))
- Recall (macro): (\frac{1}{C}\sum_{i=0}^{C-1} R(i))
Weighted-Averaging
Weighted averaging computes the metrics for each class and then takes the
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