DTM-based Filtrations
Fuente:
arXiv
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| Hauptverfasser: | , , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866914626615115776 |
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| author | Anai, Hirokazu Chazal, Frédéric Glisse, Marc Ike, Yuichi Inakoshi, Hiroya Tinarrage, Raphaël Umeda, Yuhei |
| author_facet | Anai, Hirokazu Chazal, Frédéric Glisse, Marc Ike, Yuichi Inakoshi, Hiroya Tinarrage, Raphaël Umeda, Yuhei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_04757 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | DTM-based Filtrations Anai, Hirokazu Chazal, Frédéric Glisse, Marc Ike, Yuichi Inakoshi, Hiroya Tinarrage, Raphaël Umeda, Yuhei Computational Geometry Algebraic Topology 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. |
| title | DTM-based Filtrations |
| topic | Computational Geometry Algebraic Topology |
| url | https://arxiv.org/abs/1811.04757 |