Classification between most probable classes - what is its proper name? I have to classify data between N classes.
At the first step, I make a classification between N classes with low threshold (for example, 10%). When first step is over, I have $M$ labels assigned to my datum $(M \leqslant N)$.
At the second step, I make normal classification with normal threshold between the $M$ classes to get the final decision.
What is the proper name of such policy?
 A: Many problems are caused by classification or premature classification.  Think about using a continuous probability accuracy scoring rule.  If you are interested in that I can send you a good reference.
A: I think the name is going to largely depend on how exactly you carry out the process, so unfortunately the best I'll be able to do is throw some keywords at you with a little context. 
Do you use the $M$ outputs of the first classifier as features for the second? If so this sounds like Cascading Classifiers. I think this term would also include the case where you did something like had a different classifier for each of the $\binom{N}{M}$ possible results of the first step. 
Another term you might look at is stacking, although this doesn't really sound like what you're after.
A: In my opinion, if there exist $N$ classes and after classification you realize that only $M\leq N$ are present in your result, then it is intuitive to think that your classification can be improved by using only $M$ classes.
However this is dangerous as if your data is supposed to have $N$ classes, the fact that a certain set has $M$ classes does not mean you can assume that your classifier may have $M$ classes because you are missing information for future data.
First of all, and answering your question, I do not think your procedure is a proper policy.
On the other hand, if during classification you want to gather several classes into one (since they have few representatives for instance) you are using similar to 'pruning' in decision tree like a 'merge' of classes. Maybe that is the name you are looking for.
