A Kernel for Multi-Parameter Persistent Homology

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

Research output: Contribution to conferencePosterResearch

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

Fingerprint

Learning systems

Keywords

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

Cite this

Corbet, R., Fugacci, U., Kerber, M., Landi, C., & Wang, B. (2018). A Kernel for Multi-Parameter Persistent Homology. Poster session presented at Algebraic Topology: Methods, Computation and Science, Klosterneuburg, Austria.

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

2018. Poster session presented at Algebraic Topology: Methods, Computation and Science, Klosterneuburg, Austria.

Research output: Contribution to conferencePosterResearch

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