A Kernel for Multi-Parameter Persistent Homology

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

Research output: Contribution to conferencePaper

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.
Original languageEnglish
Publication statusPublished - 2019
EventShape Modeling International (SMI) - Simon Fraser University, Vancouver, Canada
Duration: 19 Jun 201921 Jun 2019

Conference

ConferenceShape Modeling International (SMI)
CountryCanada
CityVancouver
Period19/06/1921/06/19

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