The DD$^G$-classifier in the functional setting

The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some issues still remain. This paper is devoted to extending the DD-classifier in the following ways: first, to surpass the limitation of the DD-classifier when more than two groups are involved. Second to apply regular classification methods (like $k$NN, linear or quadratic classifiers, recursive partitioning,...) to DD-plots to obtain useful insights through the diagnostics of these methods. And third, to integrate different sources of information (data depths or multivariate functional data) in a unified way in the classification procedure. Besides, as the DD-classifier trick is especially useful in the functional framework, an enhanced revision of several functional data depths is done in the paper. A simulation study and applications to some classical real datasets are also provided showing the power of the new proposal.