On the Bootstrap for Persistence Diagrams and Landscapes
<p>Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separa...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2013-01-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | http://mais-journal.ru/jour/article/view/162 |
| _version_ | 1828081609198272512 |
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| author | F. Chazal B.T. Fasy F. Lecci A. Rinaldo A. Singh L. Wasserman |
| author_facet | F. Chazal B.T. Fasy F. Lecci A. Rinaldo A. Singh L. Wasserman |
| author_sort | F. Chazal |
| collection | DOAJ |
| description | <p>Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence diagrams and confi- dence bands for persistence landscapes.</p><p>The article is published in the author’s wording.</p> |
| first_indexed | 2024-04-11T03:37:25Z |
| format | Article |
| id | doaj.art-171b6f50932f4bfa94d23250232c728d |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-11T03:37:25Z |
| publishDate | 2013-01-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-171b6f50932f4bfa94d23250232c728d2023-01-02T04:37:11ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-01-01206111120156On the Bootstrap for Persistence Diagrams and LandscapesF. Chazal0B.T. Fasy1F. Lecci2A. Rinaldo3A. Singh4L. Wasserman5Geometrica INRIA SaclayУниверситет ТулейнУниверситет Карнеги-МеллонУниверситет Карнеги-МеллонУниверситет Карнеги-МеллонУниверситет Карнеги-Меллон<p>Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence diagrams and confi- dence bands for persistence landscapes.</p><p>The article is published in the author’s wording.</p>http://mais-journal.ru/jour/article/view/162устойчивые гомологиизагрузчиктопологический анализ данных |
| spellingShingle | F. Chazal B.T. Fasy F. Lecci A. Rinaldo A. Singh L. Wasserman On the Bootstrap for Persistence Diagrams and Landscapes Моделирование и анализ информационных систем устойчивые гомологии загрузчик топологический анализ данных |
| title | On the Bootstrap for Persistence Diagrams and Landscapes |
| title_full | On the Bootstrap for Persistence Diagrams and Landscapes |
| title_fullStr | On the Bootstrap for Persistence Diagrams and Landscapes |
| title_full_unstemmed | On the Bootstrap for Persistence Diagrams and Landscapes |
| title_short | On the Bootstrap for Persistence Diagrams and Landscapes |
| title_sort | on the bootstrap for persistence diagrams and landscapes |
| topic | устойчивые гомологии загрузчик топологический анализ данных |
| url | http://mais-journal.ru/jour/article/view/162 |
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