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DOI: 10.4230/LIPIcs.SoCG.2019.58
URN: urn:nbn:de:0030-drops-104623
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10462/
Anai, Hirokazu ; Chazal, Frédéric ; Glisse, Marc ; Ike, Yuichi ; Inakoshi, Hiroya ; Tinarrage, Raphaël ; Umeda, Yuhei
DTM-Based Filtrations
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Abstract
Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Cech 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.
BibTeX - Entry
@InProceedings{anai_et_al:LIPIcs:2019:10462,
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},
title = {{DTM-Based Filtrations}},
booktitle = {35th International Symposium on Computational Geometry (SoCG 2019)},
pages = {58:1--58:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-104-7},
ISSN = {1868-8969},
year = {2019},
volume = {129},
editor = {Gill Barequet and Yusu Wang},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10462},
URN = {urn:nbn:de:0030-drops-104623},
doi = {10.4230/LIPIcs.SoCG.2019.58},
annote = {Keywords: Topological Data Analysis, Persistent homology}
}
| Keywords: | Topological Data Analysis, Persistent homology | |
| Seminar: | 35th International Symposium on Computational Geometry (SoCG 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 11.06.2019 |
