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
N1 - Publisher Copyright:
© Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage, and Yuhei Umeda.
PY - 2019/6/1
Y1 - 2019/6/1
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.
KW - Persistent homology
KW - Topological Data Analysis
UR - https://www.scopus.com/pages/publications/85068036639
U2 - 10.4230/LIPIcs.SoCG.2019.58
DO - 10.4230/LIPIcs.SoCG.2019.58
M3 - Conference contribution
AN - SCOPUS:85068036639
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 35th International Symposium on Computational Geometry, SoCG 2019
A2 - Barequet, Gill
A2 - Wang, Yusu
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 35th International Symposium on Computational Geometry, SoCG 2019
Y2 - 18 June 2019 through 21 June 2019
ER -