A Kernel for Multi-Parameter Persistent Homology

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

Publikation: KonferenzbeitragPosterForschung

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
PublikationsstatusUnveröffentlicht - 2018
VeranstaltungAlgebraic Topology: Methods, Computation and Science - IST Austria, Klosterneuburg, Österreich
Dauer: 25 Jun 201829 Jun 2018
Konferenznummer: 8
https://ist.ac.at/atmcs8/welcome/

Konferenz

KonferenzAlgebraic Topology: Methods, Computation and Science
KurztitelATMCS
LandÖsterreich
OrtKlosterneuburg
Zeitraum25/06/1829/06/18
Internetadresse

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    Corbet, R., Fugacci, U., Kerber, M., Landi, C., & Wang, B. (2018). A Kernel for Multi-Parameter Persistent Homology. Postersitzung präsentiert bei Algebraic Topology: Methods, Computation and Science, Klosterneuburg, Österreich.

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

    2018. Postersitzung präsentiert bei Algebraic Topology: Methods, Computation and Science, Klosterneuburg, Österreich.

    Publikation: KonferenzbeitragPosterForschung

    Corbet, R, Fugacci, U, Kerber, M, Landi, C & Wang, B 2018, 'A Kernel for Multi-Parameter Persistent Homology', Klosterneuburg, Österreich, 25/06/18 - 29/06/18, .
    Corbet R, Fugacci U, Kerber M, Landi C, Wang B. A Kernel for Multi-Parameter Persistent Homology. 2018. Postersitzung präsentiert bei Algebraic Topology: Methods, Computation and Science, Klosterneuburg, Österreich.
    Corbet, René ; Fugacci, Ulderico ; Kerber, Michael ; Landi, Claudia ; Wang, Bei. / A Kernel for Multi-Parameter Persistent Homology. Postersitzung präsentiert bei Algebraic Topology: Methods, Computation and Science, Klosterneuburg, Österreich.
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