Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values
The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would allow multi-parameter persistent homology to be a viable option for data analysis. I...
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Bapat, Asilata Brooks, Robyn Hacker, Celia Landi, Claudia Mahler, Barbara I Stephenson, Elizabeth R |
| description | The exact computation of the matching distance for multi-parameter
persistence modules is an active area of research in computational topology.
Achieving an easily obtainable exact computation of this distance would allow
multi-parameter persistent homology to be a viable option for data analysis. In
this paper, we provide theoretical results for the computation of the matching
distance in two dimensions along with a geometric interpretation of the lines
through parameter space realizing this distance. The crucial point of the
method we propose is that it can be easily implemented. |
| doi_str_mv | 10.48550/arxiv.2210.12868 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2210_12868</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2210_12868</sourcerecordid><originalsourceid>FETCH-LOGICAL-a678-75fb286d2f6af8582016bbf180e3444a27619f0e96c96438d720b30ea59f52783</originalsourceid><addsrcrecordid>eNotj8tOwzAURL1hgQofwAr_QIrfdpYoPKVWdFHBMrpJrqmlpKlsB8HfkxRWo5mRRnMIueFsrZzW7A7id_haCzEHXDjjLslHNQ6nKYfjJ80HpFvI7WExDyFlOLZIR09FsYMIA2aMdIcxzRUu1Xbsph4T9XEcaBVDDi309B36CdMVufDQJ7z-1xXZPz3uq5di8_b8Wt1vCjDWFVb7Zv7RCW_AO-0E46ZpPHcMpVIKhDW89AxL05ZGSddZwRrJEHTptbBOrsjt3-yZrD7FMED8qRfC-kwofwFUxEsU</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values</title><source>arXiv.org</source><creator>Bapat, Asilata ; Brooks, Robyn ; Hacker, Celia ; Landi, Claudia ; Mahler, Barbara I ; Stephenson, Elizabeth R</creator><creatorcontrib>Bapat, Asilata ; Brooks, Robyn ; Hacker, Celia ; Landi, Claudia ; Mahler, Barbara I ; Stephenson, Elizabeth R</creatorcontrib><description>The exact computation of the matching distance for multi-parameter
persistence modules is an active area of research in computational topology.
Achieving an easily obtainable exact computation of this distance would allow
multi-parameter persistent homology to be a viable option for data analysis. In
this paper, we provide theoretical results for the computation of the matching
distance in two dimensions along with a geometric interpretation of the lines
through parameter space realizing this distance. The crucial point of the
method we propose is that it can be easily implemented.</description><identifier>DOI: 10.48550/arxiv.2210.12868</identifier><language>eng</language><subject>Computer Science - Computational Geometry ; Mathematics - Algebraic Topology</subject><creationdate>2022-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2210.12868$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2210.12868$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bapat, Asilata</creatorcontrib><creatorcontrib>Brooks, Robyn</creatorcontrib><creatorcontrib>Hacker, Celia</creatorcontrib><creatorcontrib>Landi, Claudia</creatorcontrib><creatorcontrib>Mahler, Barbara I</creatorcontrib><creatorcontrib>Stephenson, Elizabeth R</creatorcontrib><title>Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values</title><description>The exact computation of the matching distance for multi-parameter
persistence modules is an active area of research in computational topology.
Achieving an easily obtainable exact computation of this distance would allow
multi-parameter persistent homology to be a viable option for data analysis. In
this paper, we provide theoretical results for the computation of the matching
distance in two dimensions along with a geometric interpretation of the lines
through parameter space realizing this distance. The crucial point of the
method we propose is that it can be easily implemented.</description><subject>Computer Science - Computational Geometry</subject><subject>Mathematics - Algebraic Topology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tOwzAURL1hgQofwAr_QIrfdpYoPKVWdFHBMrpJrqmlpKlsB8HfkxRWo5mRRnMIueFsrZzW7A7id_haCzEHXDjjLslHNQ6nKYfjJ80HpFvI7WExDyFlOLZIR09FsYMIA2aMdIcxzRUu1Xbsph4T9XEcaBVDDi309B36CdMVufDQJ7z-1xXZPz3uq5di8_b8Wt1vCjDWFVb7Zv7RCW_AO-0E46ZpPHcMpVIKhDW89AxL05ZGSddZwRrJEHTptbBOrsjt3-yZrD7FMED8qRfC-kwofwFUxEsU</recordid><startdate>20221023</startdate><enddate>20221023</enddate><creator>Bapat, Asilata</creator><creator>Brooks, Robyn</creator><creator>Hacker, Celia</creator><creator>Landi, Claudia</creator><creator>Mahler, Barbara I</creator><creator>Stephenson, Elizabeth R</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20221023</creationdate><title>Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values</title><author>Bapat, Asilata ; Brooks, Robyn ; Hacker, Celia ; Landi, Claudia ; Mahler, Barbara I ; Stephenson, Elizabeth R</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-75fb286d2f6af8582016bbf180e3444a27619f0e96c96438d720b30ea59f52783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Computational Geometry</topic><topic>Mathematics - Algebraic Topology</topic><toplevel>online_resources</toplevel><creatorcontrib>Bapat, Asilata</creatorcontrib><creatorcontrib>Brooks, Robyn</creatorcontrib><creatorcontrib>Hacker, Celia</creatorcontrib><creatorcontrib>Landi, Claudia</creatorcontrib><creatorcontrib>Mahler, Barbara I</creatorcontrib><creatorcontrib>Stephenson, Elizabeth R</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bapat, Asilata</au><au>Brooks, Robyn</au><au>Hacker, Celia</au><au>Landi, Claudia</au><au>Mahler, Barbara I</au><au>Stephenson, Elizabeth R</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values</atitle><date>2022-10-23</date><risdate>2022</risdate><abstract>The exact computation of the matching distance for multi-parameter
persistence modules is an active area of research in computational topology.
Achieving an easily obtainable exact computation of this distance would allow
multi-parameter persistent homology to be a viable option for data analysis. In
this paper, we provide theoretical results for the computation of the matching
distance in two dimensions along with a geometric interpretation of the lines
through parameter space realizing this distance. The crucial point of the
method we propose is that it can be easily implemented.</abstract><doi>10.48550/arxiv.2210.12868</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2210.12868 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2210_12868 |
| source | arXiv.org |
| subjects | Computer Science - Computational Geometry Mathematics - Algebraic Topology |
| title | Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T05%3A01%3A27IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Computing%20the%20Matching%20Distance%20of%202-Parameter%20Persistence%20Modules%20from%20Critical%20Values&rft.au=Bapat,%20Asilata&rft.date=2022-10-23&rft_id=info:doi/10.48550/arxiv.2210.12868&rft_dat=%3Carxiv_GOX%3E2210_12868%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |