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

TL;DR

This paper extends the DD-classifier to handle multiple groups, integrates traditional classification methods with DD-plots for better diagnostics, and combines various data sources, especially in functional data analysis, with demonstrated effectiveness.

Contribution

The paper introduces a multi-group extension of the DD-classifier, incorporates standard classifiers into DD-plot diagnostics, and unifies different data sources in a functional data context.

Findings

Enhanced DD-classifier handles multiple groups effectively.

Integration of classical classifiers improves diagnostic insights.

Simulation and real data applications demonstrate improved classification power.

Abstract

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.