Theory of angular depth for classification of directional data

Stanislav Nagy (), Houyem Demni (), Davide Buttarazzi () and Giovanni C. Porzio ()
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Stanislav Nagy: Charles University
Houyem Demni: University of Cassino and Southern Lazio
Davide Buttarazzi: University of Cassino and Southern Lazio
Giovanni C. Porzio: University of Cassino and Southern Lazio

Advances in Data Analysis and Classification, 2024, vol. 18, issue 3, No 5, 627-662

Abstract: Abstract Depth functions offer an array of tools that enable the introduction of quantile- and ranking-like approaches to multivariate and non-Euclidean datasets. We investigate the potential of using depths in the problem of nonparametric supervised classification of directional data, that is classification of data that naturally live on the unit sphere of a Euclidean space. In this paper, we address the problem mainly from a theoretical side, with the final goal of offering guidelines on which angular depth function should be adopted in classifying directional data. A set of desirable properties of an angular depth is put forward. With respect to these properties, we compare and contrast the most widely used angular depth functions. Simulated and real data are eventually exploited to showcase the main implications of the discussed theoretical results, with an emphasis on potentials and limits of the often disregarded angular halfspace depth.

Keywords: Angular depth; Directional data; Hyperspheres; Statistical depth; Supervised classification; 62H11; 62H30; 62G05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11634-023-00557-3

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