Difference between ROC-AUC and Multiclass AUC (MAUC) I am trying to understand the interpretation of these metrics in a multiclass scenario: ROC-AUC and MAUC. Scikit-learn provides an implementation for ROC-AUC score, which can be used for both binary and multiclass problems.
However, some studies such as 2, 3, 4 and 5 suggest averaging class-wise AUC in multiclass.
My experiments with this metrics yield different results. Do they then evaluate to different quantities?
For clarity, I used 4 implementation as well as sklearn's ROC-AUC. I the case of  sklearn's, I set the hyperparameters as:
roc_auc = metrics.roc_auc_score(y_test, ypred, average='weighted', 
    multi_class='ovo',labels=labels)

With Random Forest classifier, we obtained:
ROC-AUC:  0.58 # sklearn's roc-auc-score
MAUC:     0.69

This is more than a 10% difference so the two values are not close at all.
EDIT
References:
1 sklearn's roc-auc score: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.roc_auc_score.html
2 Tanha, J., Abdi, Y., Samadi, N., Razzaghi, N., Asadpour, M.: Boosting methods
for multi-class imbalanced data classification: an experimental review. Journal of
Big Data 7(1), 1–47 (2020)
3 Wang, R., Tang, K.: An empirical study of MAUC in multi-class
problems with uncertain cost matrices. CoRR abs/1209.1800 (2012),
http://arxiv.org/abs/1209.1800
4 https://gist.github.com/stulacy/672114792371dc13b247
5 https://github.com/pritomsaha/Multiclass_AUC/blob/master/multiclass_auc.ipynb

Reference [5] seems to use an approximation in the function a_value but that doesn't seem to be the way the AUC is calculated in sklearn. It uses the method _average_multiclass_ovo_score, whose binary_metric is given as _binary_roc_auc_score. This method calls the roc_curve and general purpose auc method. I don't think this implements the logic embedded in the fourth reference.
Even the toy example given in [5] does not give the same value as sklearn.
