A Kernel for Multi-Parameter Persistent Homology

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

A Kernel for Multi-Parameter Persistent Homology

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

Institut für Geometrie (5070)

Publikation: Konferenzbeitrag › Paper

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.

Originalsprache	englisch
Publikationsstatus	Veröffentlicht - 2019
Veranstaltung	Shape Modeling International (SMI) - Simon Fraser University, Vancouver, Kanada Dauer: 19 Jun 2019 → 21 Jun 2019

Konferenz

Konferenz	Shape Modeling International (SMI)
Land	Kanada
Ort	Vancouver
Zeitraum	19/06/19 → 21/06/19

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title = "A Kernel for Multi-Parameter Persistent Homology",

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.",

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T1 - A Kernel for Multi-Parameter Persistent Homology

AU - Corbet, René

AU - Fugacci, Ulderico

AU - Kerber, Michael

AU - Landi, Claudia

AU - Wang, Bei

PY - 2019

Y1 - 2019

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.

M3 - Paper

ER -