{"id":"https://openalex.org/W4406458113","doi":"https://doi.org/10.1109/bigdata62323.2024.10825374","title":"Piecewise Computation of Persistent Homology","display_name":"Piecewise Computation of Persistent Homology","publication_year":2024,"publication_date":"2024-12-15","ids":{"openalex":"https://openalex.org/W4406458113","doi":"https://doi.org/10.1109/bigdata62323.2024.10825374"},"language":"en","primary_location":{"id":"doi:10.1109/bigdata62323.2024.10825374","is_oa":false,"landing_page_url":"https://doi.org/10.1109/bigdata62323.2024.10825374","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Conference on Big Data (BigData)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103272629","display_name":"Rohit P. Singh","orcid":"https://orcid.org/0000-0003-2872-1232"},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rohit P. Singh","raw_affiliation_strings":["Univ of Wisconsin,Milwaukee,WI"],"affiliations":[{"raw_affiliation_string":"Univ of Wisconsin,Milwaukee,WI","institution_ids":["https://openalex.org/I43579087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053803135","display_name":"Nicholas O. Malott","orcid":"https://orcid.org/0000-0003-3848-4381"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nicholas O. Malott","raw_affiliation_strings":["Interstates,Cincinnati,OH"],"affiliations":[{"raw_affiliation_string":"Interstates,Cincinnati,OH","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011672232","display_name":"Philip A. Wilsey","orcid":"https://orcid.org/0000-0002-6562-8646"},"institutions":[{"id":"https://openalex.org/I63135867","display_name":"University of Cincinnati","ror":"https://ror.org/01e3m7079","country_code":"US","type":"education","lineage":["https://openalex.org/I63135867"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Philip A. Wilsey","raw_affiliation_strings":["Univ of Cincinnati,Cincinnati,OH"],"affiliations":[{"raw_affiliation_string":"Univ of Cincinnati,Cincinnati,OH","institution_ids":["https://openalex.org/I63135867"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103272629"],"corresponding_institution_ids":["https://openalex.org/I43579087"],"apc_list":null,"apc_paid":null,"fwci":0.3758,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68619091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"2721","last_page":"2730"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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":1.0,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9962000250816345,"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"}},{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9581000208854675,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6341809630393982},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5779411196708679},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.5084613561630249},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4675499498844147},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4327424168586731},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22248265147209167},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20867756009101868}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6341809630393982},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5779411196708679},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.5084613561630249},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4675499498844147},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4327424168586731},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22248265147209167},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20867756009101868}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/bigdata62323.2024.10825374","is_oa":false,"landing_page_url":"https://doi.org/10.1109/bigdata62323.2024.10825374","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Conference on Big Data (BigData)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":72,"referenced_works":["https://openalex.org/W66443818","https://openalex.org/W124643305","https://openalex.org/W1486210143","https://openalex.org/W1495913768","https://openalex.org/W1550314527","https://openalex.org/W1596721197","https://openalex.org/W1972098431","https://openalex.org/W1972969203","https://openalex.org/W1974993532","https://openalex.org/W1986022261","https://openalex.org/W1988925586","https://openalex.org/W1995627295","https://openalex.org/W2002165972","https://openalex.org/W2010441082","https://openalex.org/W2026940923","https://openalex.org/W2071164857","https://openalex.org/W2071391326","https://openalex.org/W2073443682","https://openalex.org/W2087841994","https://openalex.org/W2093328450","https://openalex.org/W2102692026","https://openalex.org/W2104339857","https://openalex.org/W2124511088","https://openalex.org/W2125464731","https://openalex.org/W2126751256","https://openalex.org/W2137556660","https://openalex.org/W2151631165","https://openalex.org/W2163339655","https://openalex.org/W2217669842","https://openalex.org/W2328294984","https://openalex.org/W2370347111","https://openalex.org/W2474744642","https://openalex.org/W2481594651","https://openalex.org/W2568390795","https://openalex.org/W2610774430","https://openalex.org/W2611386120","https://openalex.org/W2773695849","https://openalex.org/W2797507693","https://openalex.org/W2912764462","https://openalex.org/W2963061445","https://openalex.org/W2963082453","https://openalex.org/W2963197769","https://openalex.org/W2963336247","https://openalex.org/W2963601914","https://openalex.org/W3037960583","https://openalex.org/W3098455240","https://openalex.org/W3159302701","https://openalex.org/W3164551597","https://openalex.org/W3194339924","https://openalex.org/W3199627945","https://openalex.org/W3202868818","https://openalex.org/W4210495778","https://openalex.org/W4225271072","https://openalex.org/W4225725980","https://openalex.org/W4234555707","https://openalex.org/W4285451384","https://openalex.org/W4293370538","https://openalex.org/W4318148399","https://openalex.org/W4319585872","https://openalex.org/W4401074294","https://openalex.org/W4401418816","https://openalex.org/W6601336132","https://openalex.org/W6617749853","https://openalex.org/W6637131181","https://openalex.org/W6638638485","https://openalex.org/W6659174362","https://openalex.org/W6686900618","https://openalex.org/W6727982348","https://openalex.org/W6728167529","https://openalex.org/W6754103575","https://openalex.org/W6761023787","https://openalex.org/W6780608082"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W3128725485","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2797851727","https://openalex.org/W3159198591","https://openalex.org/W4293460689","https://openalex.org/W4281250841"],"abstract_inverted_index":{"Persistent":[0],"Homology":[1],"(PH)":[2],"is":[3,24,44,79,98,123],"a":[4,27,34,47,124,147,179],"widely":[5],"used":[6,56],"tool":[7],"of":[8,17,29,37,102,111,117,120,131,141,150,161,167,181],"Topological":[9],"Data":[10],"Analysis":[11],"(TDA)":[12],"that":[13,32,51,128,185],"measures":[14],"the":[15,53,76,100,108,118,151,162],"persistence":[16],"homological":[18],"features":[19],"present":[20],"in":[21,75,153,187],"data.":[22,38,121,132],"PH":[23,78,94,112,130,142,183],"computed":[25,81],"on":[26,95],"sequence":[28],"nested":[30,42],"sub-complexes":[31,62],"form":[33],"filtration":[35],"${{\\mathcal{K}}_{\\mathcal{F}}}$":[36],"In":[39,133],"general,":[40],"each":[41],"sub-complex":[43],"defined":[45],"by":[46,65],"scale":[48],"parameter":[49],"\u03f5":[50],"defines":[52],"connectivity":[54],"distances":[55],"to":[57,71,86,172,198],"for":[58,126,201],"its":[59,87],"construction.":[60],"These":[61],"are":[63],"arranged":[64],"increasing":[66],"distances,":[67],"\u03f5<inf":[68,72],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[69,73],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</inf>":[70],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u221e</inf>,":[74],"filtration;":[77],"then":[80],"from":[82],"${{\\mathcal{K}}_{\\mathcal{F}}}$.":[83],"However,":[84],"due":[85],"exponential":[88],"space":[89],"and":[90,177],"time":[91],"complexity,":[92],"computing":[93],"big":[96],"data":[97],"beyond":[99],"capabilities":[101],"contemporary":[103],"machines.":[104],"This":[105,192],"paper":[106,193],"explores":[107,194],"Piecewise":[109],"computation":[110],"(PwPH)":[113],"using":[114],"subset":[115],"constructions":[116],"filtrations":[119,200],"PwPH":[122,136,155,168],"framework":[125],"solutions":[127],"compute":[129,158],"some":[134,188],"embodiments,":[135,189],"can":[137,143,156,169],"be":[138,144,170],"support":[139],"computations":[140],"assembled":[145],"into":[146],"complete":[148],"picture":[149],"homologies;":[152],"others,":[154],"only":[157],"an":[159],"approximation":[160],"PH.":[163],"The":[164],"general":[165],"solution":[166],"organized":[171],"use":[173],"significantly":[174],"less":[175],"memory":[176],"provides":[178],"partition":[180],"computational":[182],"elements":[184],"is,":[186],"embarrassingly":[190],"parallel.":[191],"two":[195],"complementary":[196],"foundations":[197],"organize":[199],"PwPH.":[202]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
