Hi @zizoo -
Sorry for the delayed response here. One method you’ll find mentioned a lot for evaluating the results of multi-class classifiers is the F-measure (or F1), both micro- and macro- averaged. There a brief explanation and associated calculation in this thread on CrossValidated. Scikit-learn has a function that will calculate it for you. Incidentally, macro-averaged F1 is what Amazon ML uses.
There are also some methods to calculate multi-class ROC curves using pairwise comparison, where you look at the results of one class versus all the other classes combined. Here’s a different thread on CrossValidated that has links to some R packages for that.
Finally, here’s a Coursera video that highlights general concepts of multi-class classification using Python.
Hope all of this helps!