A stability theorem for bigraded persistence barcodes
Fuente:
arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866918136907825152 |
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| author | Bahri, Anthony Limonchenko, Ivan Panov, Taras Song, Jongbaek Stanley, Donald |
| author_facet | Bahri, Anthony Limonchenko, Ivan Panov, Taras Song, Jongbaek Stanley, Donald |
| contents | We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. We prove a stability theorem for the bigraded persistent double homology modules and barcodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14694 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A stability theorem for bigraded persistence barcodes Bahri, Anthony Limonchenko, Ivan Panov, Taras Song, Jongbaek Stanley, Donald Algebraic Topology Computational Geometry Machine Learning Combinatorics Metric Geometry Primary 57S12, 55N31, 57Z25, Secondary 13F55, 55U10 We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. We prove a stability theorem for the bigraded persistent double homology modules and barcodes. |
| title | A stability theorem for bigraded persistence barcodes |
| topic | Algebraic Topology Computational Geometry Machine Learning Combinatorics Metric Geometry Primary 57S12, 55N31, 57Z25, Secondary 13F55, 55U10 |
| url | https://arxiv.org/abs/2303.14694 |