How do you measure multi-label classification accuracy? Multi-label assignment is the task in machine learning to assign to each input value a set of categories from a fixed vocabulary where the categories need not be statistically independent, so precluding building a set of independent classifiers each classifying the inputs as belong to each of the categories or not.
Machine learning also needs a measure by which the model may be evaluated. So this is the question how do we evaluate a multi-label classifier?
We can’t use the normal recall,  accuracy and  F measures since they require a binary is it correct or not measure of each categorisation. Without such a measure we have no obvious means to evaluate models nor to measure concept drift.
Your intuition is correct. We do use other metrics for multi-label classification. The meaning of evaluation itself changes. Apart from grading the classifier on whether it classifies correctly or not, we also have to penalize it, if it chooses the wrong class appropriately. You could use the following metrics:

micro/macro averaging Recall/Precision, etc.
Hamming Loss
Subset Accuracy