Título:
Weighted lens depth: Some applications to supervised classification
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Autor:
Cholaquidis, Alejandro
Fraiman, Ricardo
Gamboa, Fabrice
Moreno, Leonardo
Fraiman, Ricardo
Gamboa, Fabrice
Moreno, Leonardo
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Artículo
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Palabras clave:
Mathematics - Statistics theory
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Año de publicación:
2020
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Resumen:
Starting with Tukey’s pioneering work in the 1970’s, the notion of depth in statistics has been widely extended especially in the last decade. These extensions include high dimensional data, functional data, and manifold-valued data. In particular, in the learning paradigm, the depth-depth method has become a useful technique. In this paper we extend the notion of lens depth to the case of data in metric spaces, and prove its main properties, with particular emphasis on the case of Riemannian manifolds, where we extend the concept of lens depth in such a way that it takes into account non-convex structures on the data distribution. Next we illustrate our results with some simulation results and also in some interesting real datasets, including pattern recognition in phylogenetic trees using the depth–depth approach.
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Publicado también en: The Canadian Journal of Statistics, 2023, 51(2): 652-673. DOI: 10.1002/cjs.11724
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arXiv
EN:
Mathematics (Statistics Theory), arXiv:2011.11140, Nov 2020
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ANII: FCE_1_2019_1_156054
Citación:
Cholaquidis, A, Fraiman, R, Gamboa, F [y otro autor]. "Weighted lens depth: Some applications to supervised classification". [Preprint]. Publicado en: Mathematics (Statistics Theory). [en línea] 2020 arXiv:2011.11140, Nov 2020. 19 h.
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Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2011.11140.pdf | Preprint | 1.93 MB | Adobe PDF |