After working for a while on this text classification problem, I realize that some documents belong to more than one class. I am using multinomial logistic regression which also provides a probability distribution over the classes (labels). I wonder if it is a good idea to use this distribution for multi labeling. For example, when the probabilities are [0.3, 0.6, 0.1] for the classes A, B, C respectively, I can label the document with the classes that have a probability for that document higher than a predefined threshold (say 0.25) .
Is this a good idea? I've made a Google search but couldn't found any document mentioning a method similar to this. How reliable is this method? What do you think?
To be more clear about my problem space, there are like 20 classes and mostly a document belongs to either one or two of these classes.