For multiclass classification(MCC) problems, metrics can be derived from the confusion matrix. Let $tp_i,tn_i,fp_i,fn_i$ denote the true positives, true negatives, false positives, false negatives respectively.
MCC problems, usually macro and micro metrics are computed:
→ Micro metrics (with subscript $\mu$ in table below) are computed by summing up individual tp, tn, fp and fn to extend the two class formula for precision and recall for MCC.
→ Macro metrics are computed by taking the average precision, recall of the system on different sets treating classifier for each class as a 1 vs all classifier.
See the table below for popular micro and macro metrics for multi class classification.
From: https://www.sciencedirect.com/science/article/pii/S0306457309000259
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