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.
LanguageEnglish
StatusUnpublished - 2018

Fingerprint

Learning systems

Keywords

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

Cite this

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

2018.

Research output: Contribution to conferencePosterResearch

Corbet, René ; Fugacci, Ulderico ; Kerber, Michael ; Landi, Claudia ; Wang, Bei. / A Kernel for Multi-Parameter Persistent Homology.
@conference{d079627fe4c64d5ea4de7ad861f1c7f0,
title = "A Kernel for Multi-Parameter Persistent Homology",
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.",
keywords = "cs.LG, cs.CG, math.AT, stat.ML",
author = "Ren{\'e} Corbet and Ulderico Fugacci and Michael Kerber and Claudia Landi and Bei Wang",
year = "2018",
language = "English",

}

TY - CONF

T1 - A Kernel for Multi-Parameter Persistent Homology

AU - Corbet, René

AU - Fugacci, Ulderico

AU - Kerber, Michael

AU - Landi, Claudia

AU - Wang, Bei

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - cs.LG

KW - cs.CG

KW - math.AT

KW - stat.ML

M3 - Poster

ER -