{"id":"https://openalex.org/W3166214348","doi":"https://doi.org/10.1007/s00454-023-00498-w","title":"Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams","display_name":"Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams","publication_year":2023,"publication_date":"2023-05-05","ids":{"openalex":"https://openalex.org/W3166214348","doi":"https://doi.org/10.1007/s00454-023-00498-w","mag":"3166214348"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-023-00498-w","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00498-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00498-w.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00498-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025846695","display_name":"Pawe\u0142 D\u0142otko","orcid":"https://orcid.org/0000-0001-5352-3102"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Pawe\u0142 D\u0142otko","raw_affiliation_strings":["Dioscuri Centre for Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656, Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0001-5352-3102","affiliations":[{"raw_affiliation_string":"Dioscuri Centre for Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656, Warsaw, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029514653","display_name":"Niklas Hellmer","orcid":"https://orcid.org/0000-0002-6500-6329"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Niklas Hellmer","raw_affiliation_strings":["Dioscuri Centre for Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656, Warsaw, Poland","Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0002-6500-6329","affiliations":[{"raw_affiliation_string":"Dioscuri Centre for Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656, Warsaw, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025846695"],"corresponding_institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I99542240"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.194,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48542884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"71","issue":"3","first_page":"1131","last_page":"1164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12107","display_name":"Leprosy Research and Treatment","score":0.951200008392334,"subfield":{"id":"https://openalex.org/subfields/2725","display_name":"Infectious Diseases"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9340999722480774,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.9530282616615295},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7681641578674316},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6342260837554932},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5338016748428345},{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.5033907294273376},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38668859004974365},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.33127203583717346},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3255544900894165},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31236550211906433},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23013383150100708},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08311334252357483}],"concepts":[{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.9530282616615295},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7681641578674316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6342260837554932},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5338016748428345},{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.5033907294273376},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38668859004974365},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33127203583717346},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3255544900894165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31236550211906433},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23013383150100708},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08311334252357483},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-023-00498-w","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00498-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00498-w.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2106.02538","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.02538","pdf_url":"https://arxiv.org/pdf/2106.02538","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-023-00498-w","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00498-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00498-w.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1132496359","display_name":"Application driven Topological Data Analysis","funder_award_id":"EP/R018472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6066696820","display_name":null,"funder_award_id":"EP/R018472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320322434","display_name":"Max-Planck-Gesellschaft","ror":"https://ror.org/01hhn8329"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3166214348.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1483679902","https://openalex.org/W1585160083","https://openalex.org/W1969883941","https://openalex.org/W1987971958","https://openalex.org/W2011301426","https://openalex.org/W2021097403","https://openalex.org/W2032916024","https://openalex.org/W2037817770","https://openalex.org/W2050204708","https://openalex.org/W2052551455","https://openalex.org/W2101234009","https://openalex.org/W2108776879","https://openalex.org/W2157529519","https://openalex.org/W2254463431","https://openalex.org/W2294510945","https://openalex.org/W2787888820","https://openalex.org/W2792401492","https://openalex.org/W2793477525","https://openalex.org/W2804231530","https://openalex.org/W2964237352","https://openalex.org/W2964292054","https://openalex.org/W3003964599","https://openalex.org/W3039948875","https://openalex.org/W3103476440","https://openalex.org/W3140579943","https://openalex.org/W3164387821","https://openalex.org/W4206471589","https://openalex.org/W6675354045"],"related_works":["https://openalex.org/W1657880117","https://openalex.org/W2595172197","https://openalex.org/W2127970246","https://openalex.org/W2084856301","https://openalex.org/W1001352512","https://openalex.org/W4382618745","https://openalex.org/W2885125400","https://openalex.org/W1989889224","https://openalex.org/W1987128138","https://openalex.org/W2381411913"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"topological":[2],"data":[3],"analysis":[4],"(TDA),":[5],"persistence":[6],"diagrams":[7],"(PDs)":[8],"have":[9],"been":[10],"a":[11,33,39,49,58,67],"successful":[12],"tool.":[13],"To":[14],"compare":[15],"them,":[16],"Wasserstein":[17,76],"and":[18,31,70,80,92],"bottleneck":[19,44,62],"distances":[20],"are":[21],"commonly":[22],"used.":[23],"We":[24,83],"address":[25],"the":[26,61,88],"shortcomings":[27],"of":[28,51,60],"these":[29],"metrics":[30,54,65,77],"show":[32],"way":[34,41],"to":[35,48,74,86],"investigate":[36],"them":[37],"in":[38],"systematic":[40],"by":[42],"introducing":[43],"profiles.":[45],"This":[46],"leads":[47],"notion":[50],"discrete":[52],"Prokhorov":[53],"for":[55],"PDs":[56],"as":[57],"generalization":[59],"distance.":[63],"These":[64],"satisfy":[66],"stability":[68],"result":[69],"can":[71],"be":[72],"used":[73],"bound":[75],"from":[78,81],"above":[79],"below.":[82],"provide":[84],"algorithms":[85],"compute":[87],"newly":[89],"introduced":[90],"quantities":[91],"end":[93],"with":[94],"an":[95],"discussion":[96],"about":[97],"experiments.":[98]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-01-20T17:24:06.736184","created_date":"2021-06-22T00:00:00"}