A Kernel for Multi-Parameter Persistent Homology

René Corbet, Ulderico Fugacci, Michael Kerber, Claudia Landi, Bei Wang

Publikation: KonferenzbeitragPaperForschungBegutachtung

Abstract

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques. We contribute a kernel construction for multi-parameter persistence by integrating a one-parameter kernel weighted along straight lines. We prove that our kernel is stable and efficiently computable, which establishes a theoretical connection between topological data analysis and machine learning for multivariate data analysis.
Originalspracheenglisch
PublikationsstatusVeröffentlicht - 2019
VeranstaltungShape Modeling International (SMI) - Simon Fraser University, Vancouver, Kanada
Dauer: 19 Jun 201921 Jun 2019

Konferenz

KonferenzShape Modeling International (SMI)
LandKanada
OrtVancouver
Zeitraum19/06/1921/06/19

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Learning systems

Dies zitieren

Corbet, R., Fugacci, U., Kerber, M., Landi, C., & Wang, B. (2019). A Kernel for Multi-Parameter Persistent Homology. Beitrag in Shape Modeling International (SMI), Vancouver, Kanada.

A Kernel for Multi-Parameter Persistent Homology. / Corbet, René; Fugacci, Ulderico; Kerber, Michael; Landi, Claudia; Wang, Bei.

2019. Beitrag in Shape Modeling International (SMI), Vancouver, Kanada.

Publikation: KonferenzbeitragPaperForschungBegutachtung

Corbet, R, Fugacci, U, Kerber, M, Landi, C & Wang, B 2019, 'A Kernel for Multi-Parameter Persistent Homology' Beitrag in Shape Modeling International (SMI), Vancouver, Kanada, 19/06/19 - 21/06/19, .
Corbet R, Fugacci U, Kerber M, Landi C, Wang B. A Kernel for Multi-Parameter Persistent Homology. 2019. Beitrag in Shape Modeling International (SMI), Vancouver, Kanada.
Corbet, René ; Fugacci, Ulderico ; Kerber, Michael ; Landi, Claudia ; Wang, Bei. / A Kernel for Multi-Parameter Persistent Homology. Beitrag in Shape Modeling International (SMI), Vancouver, Kanada.
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AU - Corbet, René

AU - Fugacci, Ulderico

AU - Kerber, Michael

AU - Landi, Claudia

AU - Wang, Bei

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N2 - Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques. We contribute a kernel construction for multi-parameter persistence by integrating a one-parameter kernel weighted along straight lines. We prove that our kernel is stable and efficiently computable, which establishes a theoretical connection between topological data analysis and machine learning for multivariate data analysis.

AB - Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques. We contribute a kernel construction for multi-parameter persistence by integrating a one-parameter kernel weighted along straight lines. We prove that our kernel is stable and efficiently computable, which establishes a theoretical connection between topological data analysis and machine learning for multivariate data analysis.

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