I have a dataset with a non-binary target class $c$. I want to compute the AUC of my classifier and can do this easily using the one-vs-rest approach. I train $\binom{n}{2}$ classifiers where n is the number of different values that $c$ can take and compute the AUC for each of those classifiers then just take the mean of different AUCs.
The problem is that sometimes, the AUC is lower than $0.5$. This seems okay to me, since this applies for binary classes and my intuition tells me I should only be worried if the overall AUC was lower than $.25$ when the target class can take 4 different values. Is this logic flawed or is my intuition right?
I've also noticed that the AUC of some of the binary classifiers is lower than $.5$. In this case it should be okay to change it to $1-AUC$ since it's a binary classifier, or will this mess up the general result.
Any insights would be appreciated. Is my approach correct or am I messing up the overall score with my tampering?
