A Kernel for Multi-Parameter Persistent Homology

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

Research output: Contribution to conferencePoster

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 statusUnpublished - 2018
EventAlgebraic Topology: Methods, Computation and Science - IST Austria, Klosterneuburg, Austria
Duration: 25 Jun 201829 Jun 2018
Conference number: 8
https://ist.ac.at/atmcs8/welcome/

Conference

ConferenceAlgebraic Topology: Methods, Computation and Science
Abbreviated titleATMCS
CountryAustria
CityKlosterneuburg
Period25/06/1829/06/18
Internet address

Keywords

  • cs.LG
  • cs.CG
  • math.AT
  • stat.ML

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