A Kernel for Multi-Parameter Persistent Homology

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

A Kernel for Multi-Parameter Persistent Homology

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

Institute of Geometry (5070)

Research output: Contribution to conference › Poster

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 language	English
Publication status	Unpublished - 2018
Event	Algebraic Topology: Methods, Computation and Science - IST Austria, Klosterneuburg, Austria Duration: 25 Jun 2018 → 29 Jun 2018 Conference number: 8 https://ist.ac.at/atmcs8/welcome/

Conference

Conference	Algebraic Topology: Methods, Computation and Science
Abbreviated title	ATMCS
Country/Territory	Austria
City	Klosterneuburg
Period	25/06/18 → 29/06/18
Internet address	https://ist.ac.at/atmcs8/welcome/

Keywords

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

Cite this

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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. ",

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author = "Ren{\'e} Corbet and Ulderico Fugacci and Michael Kerber and Claudia Landi and Bei Wang",

year = "2018",

language = "English",

note = "Algebraic Topology: Methods, Computation and Science, ATMCS ; Conference date: 25-06-2018 Through 29-06-2018",

url = "https://ist.ac.at/atmcs8/welcome/",

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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

N1 - Conference code: 8

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

T2 - Algebraic Topology: Methods, Computation and Science

Y2 - 25 June 2018 through 29 June 2018

ER -

A Kernel for Multi-Parameter Persistent Homology

Abstract

Conference

Keywords

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Cite this