### Resumé

Originalsprog | Engelsk |
---|---|

Tidsskrift | Journal of Computational and Graphical Statistics |

Antal sider | 45 |

ISSN | 1061-8600 |

DOI | |

Status | E-pub ahead of print - 2019 |

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*Journal of Computational and Graphical Statistics*. https://doi.org/10.1080/10618600.2019.1573686

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*Journal of Computational and Graphical Statistics*. https://doi.org/10.1080/10618600.2019.1573686

**The accumulated persistence function, a new useful functional summary statistic for topological data analysis, with a view to brain artery trees and spatial point process applications.** / Biscio, Christophe Ange Napoléon; Møller, Jesper.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - The accumulated persistence function, a new useful functional summary statistic for topological data analysis, with a view to brain artery trees and spatial point process applications.

AU - Biscio, Christophe Ange Napoléon

AU - Møller, Jesper

PY - 2019

Y1 - 2019

N2 - We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R code used for all examples.

AB - We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R code used for all examples.

KW - clustering

KW - confindence region

KW - global rank envelope

KW - functional boxplot

KW - persitent homology

KW - two-sample test

U2 - 10.1080/10618600.2019.1573686

DO - 10.1080/10618600.2019.1573686

M3 - Journal article

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

ER -