AUC for multiclass classification

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Sepp on 26 Aug 2018
Edited: Sepp on 26 Aug 2018
Hello everybody
Let's assume that we have a classification problem with 3 classes and that we have highly imbalanced data. Let's say in class 1 we have 185 data points, in class 2 199 and in class 3 720.
For calculating the AUC on a multiclass problem there is the macro-average (giving equal weight to the classification of each label) and micro-average method (considering each element of the label indicator matrix as a binary predictio).
For such imbalanced dataset should micro-averaging or macro-averaging of AUC be used?
I'm unsure because when we have a confusion matrix as shown below, I'm getting a micro-averaged AUC of 0.76 and a macro-averaged AUC of 0.55.

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