What are evaluation metrics for multi-class classification problem ?

Multi-class classification evaluation can be done in either of the following ways :

  1. Average precision of each class, average recall of each class treating classifier for each class as one vs all classifier.
  2. Average of accuracy of each class treating the classifier for each class as a one-vs-all classifier
  3. Sum of all true positive entries in the confusion matrix (left to right diagonal) divided by the sum of total true positives and true negatives of each class in the confusion matrix.

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 for class i.

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.

Image Source : Science direct 

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