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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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.

Original language	English
Title of host publication	Topological Data Analysis - The Abel Symposium, 2018
Editors	Nils A. Baas, Gereon Quick, Markus Szymik, Marius Thaule, Gunnar E. Carlsson
Publisher	Springer
Pages	33-66
Number of pages	34
ISBN (Print)	9783030434076
DOIs	https://doi.org/10.1007/978-3-030-43408-3_2
Publication status	Published - 1 Jan 2020
Externally published	Yes
Event	Abel Symposium, 2018 - Geiranger, Norway Duration: 4 Jun 2018 → 8 Jun 2018

Publication series

Name	Abel Symposia
Volume	15
ISSN (Print)	2193-2808
ISSN (Electronic)	2197-8549

Conference

Conference	Abel Symposium, 2018
Country/Territory	Norway
City	Geiranger
Period	4/06/18 → 8/06/18

Access to Document

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

Cite this

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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).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

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