Affinity and distance. On the Newtonian structure of some data kernels

Autores
Aimar, Hugo Alejandro; Gomez, Ivana Daniela
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let X be a set. Let K(x, y) > 0 be a measure of the affinity between the data points x and y. We prove that K has the structure of a Newtonian potential K(x, y) = φ(d(x, y)) with φ decreasing and d a quasi-metric on X under two mild conditions on K. The first is that the affinity of each x to itself is infinite and that for x ≠ y the affinity is positive and finite. The second is a quantitative transitivity; if the affinity between x and y is larger than λ > 0 and the affinity of y and z is also larger than λ, then the affinity between x and z is larger than ν(λ). The function ν is concave, increasing, continuous from R+ onto R+ with ν(λ) < λ for every λ >0.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
AFFINITY KERNEL
METRIC SPACES
UNIFORM SPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/88699
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Affinity and distance. On the Newtonian structure of some data kernelsAimar, Hugo AlejandroGomez, Ivana DanielaAFFINITY KERNELMETRIC SPACESUNIFORM SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let X be a set. Let K(x, y) > 0 be a measure of the affinity between the data points x and y. We prove that K has the structure of a Newtonian potential K(x, y) = φ(d(x, y)) with φ decreasing and d a quasi-metric on X under two mild conditions on K. The first is that the affinity of each x to itself is infinite and that for x ≠ y the affinity is positive and finite. The second is a quantitative transitivity; if the affinity between x and y is larger than λ > 0 and the affinity of y and z is also larger than λ, then the affinity between x and z is larger than ν(λ). The function ν is concave, increasing, continuous from R+ onto R+ with ν(λ) < λ for every λ >0.Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaDe Gruyter Open Ltd2018-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/88699Aimar, Hugo Alejandro; Gomez, Ivana Daniela; Affinity and distance. On the Newtonian structure of some data kernels; De Gruyter Open Ltd; Analysis and Geometry in Metric Spaces; 6; 1; 2-2018; 89-952299-32742299-3274CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.degruyter.com/view/j/agms.2018.6.issue-1/agms-2018-0005/agms-2018-0005.xmlinfo:eu-repo/semantics/altIdentifier/doi/10.1515/agms-2018-0005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-23T13:59:20Zoai:ri.conicet.gov.ar:11336/88699instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-12-23 13:59:21.019CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Affinity and distance. On the Newtonian structure of some data kernels
title Affinity and distance. On the Newtonian structure of some data kernels
spellingShingle Affinity and distance. On the Newtonian structure of some data kernels
Aimar, Hugo Alejandro
AFFINITY KERNEL
METRIC SPACES
UNIFORM SPACES
title_short Affinity and distance. On the Newtonian structure of some data kernels
title_full Affinity and distance. On the Newtonian structure of some data kernels
title_fullStr Affinity and distance. On the Newtonian structure of some data kernels
title_full_unstemmed Affinity and distance. On the Newtonian structure of some data kernels
title_sort Affinity and distance. On the Newtonian structure of some data kernels
dc.creator.none.fl_str_mv Aimar, Hugo Alejandro
Gomez, Ivana Daniela
author Aimar, Hugo Alejandro
author_facet Aimar, Hugo Alejandro
Gomez, Ivana Daniela
author_role author
author2 Gomez, Ivana Daniela
author2_role author
dc.subject.none.fl_str_mv AFFINITY KERNEL
METRIC SPACES
UNIFORM SPACES
topic AFFINITY KERNEL
METRIC SPACES
UNIFORM SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let X be a set. Let K(x, y) > 0 be a measure of the affinity between the data points x and y. We prove that K has the structure of a Newtonian potential K(x, y) = φ(d(x, y)) with φ decreasing and d a quasi-metric on X under two mild conditions on K. The first is that the affinity of each x to itself is infinite and that for x ≠ y the affinity is positive and finite. The second is a quantitative transitivity; if the affinity between x and y is larger than λ > 0 and the affinity of y and z is also larger than λ, then the affinity between x and z is larger than ν(λ). The function ν is concave, increasing, continuous from R+ onto R+ with ν(λ) < λ for every λ >0.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description Let X be a set. Let K(x, y) > 0 be a measure of the affinity between the data points x and y. We prove that K has the structure of a Newtonian potential K(x, y) = φ(d(x, y)) with φ decreasing and d a quasi-metric on X under two mild conditions on K. The first is that the affinity of each x to itself is infinite and that for x ≠ y the affinity is positive and finite. The second is a quantitative transitivity; if the affinity between x and y is larger than λ > 0 and the affinity of y and z is also larger than λ, then the affinity between x and z is larger than ν(λ). The function ν is concave, increasing, continuous from R+ onto R+ with ν(λ) < λ for every λ >0.
publishDate 2018
dc.date.none.fl_str_mv 2018-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/88699
Aimar, Hugo Alejandro; Gomez, Ivana Daniela; Affinity and distance. On the Newtonian structure of some data kernels; De Gruyter Open Ltd; Analysis and Geometry in Metric Spaces; 6; 1; 2-2018; 89-95
2299-3274
2299-3274
CONICET Digital
CONICET
url http://hdl.handle.net/11336/88699
identifier_str_mv Aimar, Hugo Alejandro; Gomez, Ivana Daniela; Affinity and distance. On the Newtonian structure of some data kernels; De Gruyter Open Ltd; Analysis and Geometry in Metric Spaces; 6; 1; 2-2018; 89-95
2299-3274
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.degruyter.com/view/j/agms.2018.6.issue-1/agms-2018-0005/agms-2018-0005.xml
info:eu-repo/semantics/altIdentifier/doi/10.1515/agms-2018-0005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv De Gruyter Open Ltd
publisher.none.fl_str_mv De Gruyter Open Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.952241

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