Transform multi-label problem to multi-class problem
A multi-label problem is when an instance can have several labels, for instance a system which classifies news articles by topic could do this:


instance 1: politics, society
instance 2: sports
instance 3: culture, sports
instance 4: society
...


To turn this into a multiclass problem and still do the exact same task, one needs to create one class for each possible subset existing in the data, for instance:

{ politics-society, sports, culture-sports, society, ...}


If the original multi-labels problem contains $N$ labels, the number of classes in the multiclass problem is $2^N$ in the worst case (number of partitions of the set). 

The main problem is that the classifier needs a representative sample of every class in order to perform well. The classes sports and culture-sports (for example) are now independent from the perspective of the classifier, so the class sport cannot benefit anymore from the instances belonging to culture-sports, as it would be the case in the multi-label problem. 

So in general one would need many more instances to train a multiclass classifier than a multi-label classifier for doing the same thing.