A Kernel for Multi-Parameter Persistent Homology

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

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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 with applicability on shape analysis, recognition and classification. 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
Seiten (von - bis)100005-100016
Seitenumfang11
FachzeitschriftComputers & Graphics: X
Jahrgang2019
Ausgabenummer2
DOIs
PublikationsstatusVeröffentlicht - 1 Dez 2019

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

in: Computers & Graphics: X, Jahrgang 2019 , Nr. 2, 01.12.2019, S. 100005-100016.

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Corbet, René ; Fugacci, Ulderico ; Kerber, Michael ; Landi, Claudia ; Wang, Bei. / A Kernel for Multi-Parameter Persistent Homology. in: Computers & Graphics: X. 2019 ; Jahrgang 2019 , Nr. 2. S. 100005-100016.
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