Multiclass classification vs Binary classification with class merging: prediction accuracy

Question

I have a dataset with 4 labels. For me the most important is to be able to distinguish label 1 from all other labels, I don't care that much about distinguishing between labels 2,3 and 4. The proportions of data with each of the labels are not very different from each other (so no evident imbalance) .

I thought that merging labels 2,3,4 into a single label would make classification easier but it does not seem to be the case. The performance (of distinguishing label 1 from all the rest) with xgboost seems to be consistently better when I run multiclass classification, then when I run binary classification.

I can imagine it can be due to special geometry of the data so I wonder: does this phenomenon have a name in the literature? Is it possible to check directly for some specific data features that enable such behavior of the classifier?

Answer 1

I can imagine this happening if you were combining categories that don't have anything in common, say photos of wedding dresses, excavators, and parrots. In such a case, there is not much that the algorithm can learn about the new "category", nothing to generalize. If you want to distinguish one category from others, you could use something like one-class classification and treat this as a anomaly-detection problem. In such a case, you would use the other categories only in your test set. On another hand, if the other categories are something that you typically observe in your data, maybe there is no point in excluding relevant data, and if the multiclass classification works better, just do it.