DTM-Based Filtrations

Hirokazu Anai; Frédéric Chazal; Marc Glisse; Yuichi Ike; Hiroya Inakoshi; Raphaël Tinarrage; Yuhei Umeda

doi:10.1007/978-3-030-43408-3_2

DTM-Based Filtrations

Hirokazu Anai
, Frédéric Chazal
, Marc Glisse
, Yuichi Ike
, Hiroya Inakoshi
, Raphaël Tinarrage
, Yuhei Umeda

National Institute for Environmental Studies
INRIA

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

Résumé

Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Čech or Vietoris–Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed. In this paper, we introduce and study a new family of filtrations, the DTM-filtrations, built on top of point clouds in the Euclidean space which are more robust to noise and outliers. The approach adopted in this work relies on the notion of distance-to-measure functions, and extends some previous work on the approximation of such functions.

langue originale	Anglais
titre	Topological Data Analysis - The Abel Symposium, 2018
rédacteurs en chef	Nils A. Baas, Gereon Quick, Markus Szymik, Marius Thaule, Gunnar E. Carlsson
Editeur	Springer
Pages	33-66
Nombre de pages	34
ISBN (imprimé)	9783030434076
Les DOIs	https://doi.org/10.1007/978-3-030-43408-3_2
état	Publié - 1 janv. 2020
Modification externe	Oui
Evénement	Abel Symposium, 2018 - Geiranger, Norvcge Durée: 4 juin 2018 → 8 juin 2018

Série de publications

Nom	Abel Symposia
Volume	15
ISSN (imprimé)	2193-2808
ISSN (Electronique)	2197-8549

Une conférence

Une conférence	Abel Symposium, 2018
Pays/Territoire	Norvcge
La ville	Geiranger
période	4/06/18 → 8/06/18

Accès au document

10.1007/978-3-030-43408-3_2

Contient cette citation

@inproceedings{5476b80dd5854722801b2975a4dd1f83,

title = "DTM-Based Filtrations",

abstract = "Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the {\v C}ech or Vietoris–Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed. In this paper, we introduce and study a new family of filtrations, the DTM-filtrations, built on top of point clouds in the Euclidean space which are more robust to noise and outliers. The approach adopted in this work relies on the notion of distance-to-measure functions, and extends some previous work on the approximation of such functions.",

author = "Hirokazu Anai and Fr{\'e}d{\'e}ric Chazal and Marc Glisse and Yuichi Ike and Hiroya Inakoshi and Rapha{\"e}l Tinarrage and Yuhei Umeda",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; Abel Symposium, 2018 ; Conference date: 04-06-2018 Through 08-06-2018",

year = "2020",

month = jan,

day = "1",

doi = "10.1007/978-3-030-43408-3\_2",

language = "English",

isbn = "9783030434076",

series = "Abel Symposia",

publisher = "Springer",

pages = "33--66",

editor = "Baas, \{Nils A.\} and Gereon Quick and Markus Szymik and Marius Thaule and Carlsson, \{Gunnar E.\}",

booktitle = "Topological Data Analysis - The Abel Symposium, 2018",

}

DTM-Based Filtrations. / Anai, Hirokazu; Chazal, Frédéric; Glisse, Marc et al.
Topological Data Analysis - The Abel Symposium, 2018. Ed. / Nils A. Baas; Gereon Quick; Markus Szymik; Marius Thaule; Gunnar E. Carlsson. Springer, 2020. p. 33-66 (Abel Symposia; Vol 15).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

TY - GEN

T1 - DTM-Based Filtrations

AU - Anai, Hirokazu

AU - Chazal, Frédéric

AU - Glisse, Marc

AU - Ike, Yuichi

AU - Inakoshi, Hiroya

AU - Tinarrage, Raphaël

AU - Umeda, Yuhei

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Čech or Vietoris–Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed. In this paper, we introduce and study a new family of filtrations, the DTM-filtrations, built on top of point clouds in the Euclidean space which are more robust to noise and outliers. The approach adopted in this work relies on the notion of distance-to-measure functions, and extends some previous work on the approximation of such functions.

AB - Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Čech or Vietoris–Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed. In this paper, we introduce and study a new family of filtrations, the DTM-filtrations, built on top of point clouds in the Euclidean space which are more robust to noise and outliers. The approach adopted in this work relies on the notion of distance-to-measure functions, and extends some previous work on the approximation of such functions.

U2 - 10.1007/978-3-030-43408-3_2

DO - 10.1007/978-3-030-43408-3_2

M3 - Conference contribution

AN - SCOPUS:85087784121

SN - 9783030434076

T3 - Abel Symposia

SP - 33

EP - 66

BT - Topological Data Analysis - The Abel Symposium, 2018

A2 - Baas, Nils A.

A2 - Quick, Gereon

A2 - Szymik, Markus

A2 - Thaule, Marius

A2 - Carlsson, Gunnar E.

PB - Springer

T2 - Abel Symposium, 2018

Y2 - 4 June 2018 through 8 June 2018

ER -

DTM-Based Filtrations

Résumé

Série de publications

Une conférence

Accès au document

Empreinte digitale

Contient cette citation