A Kernel for Multi-Parameter Persistent Homology

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

Research output: Contribution to conferenceAbstract

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
Event34th International Symposium on Computational Geometry, SoCG 2018 - Budapest, Hungary
Duration: 11 Jun 201814 Jun 2018

Conference

Conference34th International Symposium on Computational Geometry, SoCG 2018
CountryHungary
CityBudapest
Period11/06/1814/06/18

Keywords

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

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