Weighted lens depth: Some applications to supervised classification
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.
| 2020 | |
| ANII: FCE_1_2019_1_156054 | |
| Mathematics - Statistics theory | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/37377 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522795396005888 |
|---|---|
| author | Cholaquidis, Alejandro |
| author2 | Fraiman, Ricardo Gamboa, Fabrice Moreno, Leonardo |
| author2_role | author author author |
| author_facet | Cholaquidis, Alejandro Fraiman, Ricardo Gamboa, Fabrice Moreno, Leonardo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Fraiman Ricardo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Gamboa Fabrice, Institut de Mathématiques de Toulouse Moreno Leonardo, Universidad de la República (Uruguay). FCEA |
| dc.creator.none.fl_str_mv | Cholaquidis, Alejandro Fraiman, Ricardo Gamboa, Fabrice Moreno, Leonardo |
| dc.date.accessioned.none.fl_str_mv | 2023-06-02T14:31:09Z |
| dc.date.available.none.fl_str_mv | 2023-06-02T14:31:09Z |
| dc.date.issued.none.fl_str_mv | 2020 |
| dc.description.abstract.none.fl_txt_mv | 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. |
| dc.description.es.fl_txt_mv | Publicado también en: The Canadian Journal of Statistics, 2023, 51(2): 652-673. DOI: 10.1002/cjs.11724 |
| dc.description.sponsorship.none.fl_txt_mv | ANII: FCE_1_2019_1_156054 |
| dc.format.extent.es.fl_str_mv | 19 h |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | 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. |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2011.11140 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/37377 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Statistics Theory), arXiv:2011.11140, Nov 2020 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Mathematics - Statistics theory |
| dc.title.none.fl_str_mv | Weighted lens depth: Some applications to supervised classification |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | Publicado también en: The Canadian Journal of Statistics, 2023, 51(2): 652-673. DOI: 10.1002/cjs.11724 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_a71a6e78b8a0fffd0047579ad3ad7a23 |
| identifier_str_mv | 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. 10.48550/arXiv.2011.11140 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/37377 |
| publishDate | 2020 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Fraiman Ricardo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Gamboa Fabrice, Institut de Mathématiques de ToulouseMoreno Leonardo, Universidad de la República (Uruguay). FCEA2023-06-02T14:31:09Z2023-06-02T14:31:09Z2020Cholaquidis, 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.https://hdl.handle.net/20.500.12008/3737710.48550/arXiv.2011.11140Publicado también en: The Canadian Journal of Statistics, 2023, 51(2): 652-673. DOI: 10.1002/cjs.11724Starting 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.Submitted by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-06-02T12:36:56Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2011.11140.pdf: 2018845 bytes, checksum: 6d20f4880995cf21800ab42213560e50 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-06-02T13:53:22Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2011.11140.pdf: 2018845 bytes, checksum: 6d20f4880995cf21800ab42213560e50 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-06-02T14:31:09Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2011.11140.pdf: 2018845 bytes, checksum: 6d20f4880995cf21800ab42213560e50 (MD5) Previous issue date: 2020ANII: FCE_1_2019_1_15605419 happlication/pdfenengarXivMathematics (Statistics Theory), arXiv:2011.11140, Nov 2020Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Mathematics - Statistics theoryWeighted lens depth: Some applications to supervised classificationArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaCholaquidis, AlejandroFraiman, RicardoGamboa, FabriceMoreno, LeonardoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/37377/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/37377/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Weighted lens depth: Some applications to supervised classification Cholaquidis, Alejandro Mathematics - Statistics theory |
| status_str | publishedVersion |
| title | Weighted lens depth: Some applications to supervised classification |
| title_full | Weighted lens depth: Some applications to supervised classification |
| title_fullStr | Weighted lens depth: Some applications to supervised classification |
| title_full_unstemmed | Weighted lens depth: Some applications to supervised classification |
| title_short | Weighted lens depth: Some applications to supervised classification |
| title_sort | Weighted lens depth: Some applications to supervised classification |
| topic | Mathematics - Statistics theory |
| url | https://hdl.handle.net/20.500.12008/37377 |
