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I am working on a classification problem. My algorithm involves splitting the data into several subsets based on a specific feature (e.g. number of XX) then training a classifier on each of these subsets. At test time, the incoming data will be passed to one of the trained classifiers depending this number of XX.

Would such a system be called an ensemble of classifiers or a bag of classifiers ?

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No, this isn't bagging. It could perhaps be called an ensemble of classifiers (see https://en.wikipedia.org/wiki/Ensemble_learning) but the most effective description will probably be to just describe what you are doing along the lines you listed in the question. A "name" is primarily useful as a short way to describe what you are doing. Some techniques are used so commonly that they have an accepted "name". What you are doing isn't standard and might not have any well-known "name", but that's OK -- you can describe what you are doing in a sentence or two, so just do that.

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