The Cosine Depth Distribution Classifier for Directional Data

  • Houyem DemniEmail author
  • Amor Messaoud
  • Giovanni C. Porzio
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Directions, rotations, axes, clock, or calendar measurements can be represented as angles or equivalently as unit vectors. As points lying on the boundary of circles, spheres, or hyper-spheres, they are also referred as directional data, and they require dedicated methods to be analyzed. In the framework of supervised classification, this work introduces a directional data classifier based on a data depth function. Depth functions provide an inner–outer ordering of the data in a reference space according to some centrality measure, and have appeared as a powerful tool in many fields of multivariate statistics. The recently introduced distance-based depth functions for directional data are considered here. More specifically, this work introduces a cosine depth based distribution method which aims at assigning directional data to classes, given that a training set with class labels is already available. A simulation study evaluating the performance of the proposed method is provided.



The authors wish to thank the two anonymous referees for their precious comments on a first version of this work. Thanks are also due to Giuseppe Pandolfo and Ondrej Vencalek for their valuable support and suggestions.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Houyem Demni
    • 1
    • 2
    Email author
  • Amor Messaoud
    • 3
  • Giovanni C. Porzio
    • 4
  1. 1.Institut Supérieur de Gestion de TunisUniversité de TunisTunisTunisia
  2. 2.University of Cassino and Southern LazioCassinoItaly
  3. 3.Tunis Business SchoolUniversité de TunisTunisTunisia
  4. 4.Department of Economics and LawUniversity of Cassino and Southern LazioCassinoItaly

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