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.
@InProceedings{anai_et_al:LIPIcs.SoCG.2019.58, author = {Anai, Hirokazu and Chazal, Fr\'{e}d\'{e}ric and Glisse, Marc and Ike, Yuichi and Inakoshi, Hiroya and Tinarrage, Rapha\"{e}l and Umeda, Yuhei}, 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 = {Barequet, Gill and Wang, Yusu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.58}, URN = {urn:nbn:de:0030-drops-104623}, doi = {10.4230/LIPIcs.SoCG.2019.58}, annote = {Keywords: Topological Data Analysis, Persistent homology} }
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