Distance-based directional depth classifiers: a robustness study

Abstract

Contaminated training sets can highly affect the performance of classification rules. For this reason, robust supervised classifiers have been introduced. Amongst the many, this work focuses on depth-based classifiers, a class of methods which have been proven to enjoy some robustness properties. However, no robustness studies are available for them within a directional data framework. Here, their performance under some directional contamination schemes is evaluated. A comparison with the directional Bayes rule is also provided. Different directional specific contamination scenarios are introduced and discussed: antipodality and orthogonality of the contaminated distribution mean, and the directional mean shift outlier model.

Keywords:

• DD-classifier
• Distribution depth
• Max-depth
• Spherical data
• Von Mises–Fisher

Acknowledgments

The authors wish to thank the two anonymous referees for their valuable comments which led to a considerable improvement of the present work. Thanks are also due to Mario Guarracino for his precious suggestions.

Additional information

Funding

The work of H. Demni and G.C. Porzio has been partially funded by the BiBiNet project (grant H35F21000430002) within the POR-Lazio FESR 2014–2020.