{"id":"https://openalex.org/W3029684635","doi":"https://doi.org/10.1007/s00454-020-00206-y","title":"Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives","display_name":"Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives","publication_year":2020,"publication_date":"2020-05-29","ids":{"openalex":"https://openalex.org/W3029684635","doi":"https://doi.org/10.1007/s00454-020-00206-y","mag":"3029684635"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-020-00206-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00206-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00206-y.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":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00206-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055728139","display_name":"Adam Brown","orcid":"https://orcid.org/0000-0002-0955-0119"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]},{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT","US"],"is_corresponding":true,"raw_author_name":"Adam Brown","raw_affiliation_strings":["Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT, 84112, USA","Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT, 84112, USA","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100349956","display_name":"Bei Wang","orcid":"https://orcid.org/0000-0002-9240-0700"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bei Wang","raw_affiliation_strings":["School of Computing and SCI Institute, University of Utah, 72 South Central Campus Drive, Salt Lake City, UT, 84112, USA"],"affiliations":[{"raw_affiliation_string":"School of Computing and SCI Institute, University of Utah, 72 South Central Campus Drive, Salt Lake City, UT, 84112, USA","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055728139"],"corresponding_institution_ids":["https://openalex.org/I157556583","https://openalex.org/I223532165"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.289,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6186883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"65","issue":"4","first_page":"1166","last_page":"1198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.8172118663787842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7970424890518188},{"id":"https://openalex.org/keywords/sheaf-cohomology","display_name":"Sheaf cohomology","score":0.7414782643318176},{"id":"https://openalex.org/keywords/stratification","display_name":"Stratification (seeds)","score":0.617867112159729},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.4872209131717682},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.43865087628364563},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.430077463388443},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4116145372390747},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36825305223464966},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3495340347290039},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3466663360595703},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3455468416213989},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17391356825828552},{"id":"https://openalex.org/keywords/group-cohomology","display_name":"Group cohomology","score":0.09815073013305664}],"concepts":[{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.8172118663787842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7970424890518188},{"id":"https://openalex.org/C93067474","wikidata":"https://www.wikidata.org/wiki/Q1493952","display_name":"Sheaf cohomology","level":4,"score":0.7414782643318176},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.617867112159729},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.4872209131717682},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.43865087628364563},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.430077463388443},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4116145372390747},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36825305223464966},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3495340347290039},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3466663360595703},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3455468416213989},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17391356825828552},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.09815073013305664},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C88548481","wikidata":"https://www.wikidata.org/wiki/Q2397491","display_name":"Seed dormancy","level":4,"score":0.0},{"id":"https://openalex.org/C3527866","wikidata":"https://www.wikidata.org/wiki/Q162267","display_name":"Dormancy","level":3,"score":0.0},{"id":"https://openalex.org/C100701293","wikidata":"https://www.wikidata.org/wiki/Q193838","display_name":"Germination","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-020-00206-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00206-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00206-y.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"}],"best_oa_location":{"id":"doi:10.1007/s00454-020-00206-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00206-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00206-y.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/G5923273611","display_name":null,"funder_award_id":"IIS-1513616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6099464845","display_name":"III: Medium: Collaborative Research: Topological Data Analysis for Large Network Visualization","funder_award_id":"1513616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7649787314","display_name":"Collaborative Research: ABI Innovation: A Scalable Framework for Visual Exploration and Hypotheses Extraction of Phenomics Data using Topological Analytics","funder_award_id":"1661375","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G955206456","display_name":null,"funder_award_id":"ABI-1661375","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320315473","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3029684635.pdf","grobid_xml":"https://content.openalex.org/works/W3029684635.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W13637651","https://openalex.org/W186822082","https://openalex.org/W1496383623","https://openalex.org/W1515675992","https://openalex.org/W1540633728","https://openalex.org/W1572740858","https://openalex.org/W1607787316","https://openalex.org/W1824091107","https://openalex.org/W2003267593","https://openalex.org/W2012205791","https://openalex.org/W2038900692","https://openalex.org/W2059134260","https://openalex.org/W2072204993","https://openalex.org/W2098646941","https://openalex.org/W2107605271","https://openalex.org/W2137630416","https://openalex.org/W2173753796","https://openalex.org/W2177347332","https://openalex.org/W2227800209","https://openalex.org/W2733830990","https://openalex.org/W2779909232","https://openalex.org/W2952111492","https://openalex.org/W2964207424","https://openalex.org/W3040586665","https://openalex.org/W3102754119","https://openalex.org/W3103861421","https://openalex.org/W3103907078","https://openalex.org/W3122930086","https://openalex.org/W3140579943","https://openalex.org/W4230710347","https://openalex.org/W4238123877","https://openalex.org/W4300596011"],"related_works":["https://openalex.org/W2315415245","https://openalex.org/W4245286857","https://openalex.org/W206853678","https://openalex.org/W1970133246","https://openalex.org/W4213286541","https://openalex.org/W3104267810","https://openalex.org/W4298345995","https://openalex.org/W4307218802","https://openalex.org/W4234721206","https://openalex.org/W3083857939"],"abstract_inverted_index":{"Abstract":[0],"We":[1,39],"investigate":[2],"a":[3,28,31],"sheaf-theoretic":[4,146],"interpretation":[5],"of":[6,20,27,91,125,132,167,173,181,184],"stratification":[7,21,49,109],"learning":[8,22],"from":[9,154],"geometric":[10,130,158],"and":[11,56,106,157],"topological":[12,156,174],"perspectives.":[13,159],"Our":[14],"main":[15],"result":[16],"is":[17,45,60],"the":[18,36,42,46,52,57,70,80,92,107,129,145,171,179,182],"construction":[19],"algorithms":[23],"framed":[24],"in":[25,86,112,170,187],"terms":[26],"sheaf":[29,59,168,185],"on":[30,97,128],"partially":[32],"ordered":[33],"set":[34],"with":[35,69],"Alexandroff":[37],"topology.":[38],"prove":[40],"that":[41],"resulting":[43],"decomposition":[44],"unique":[47],"minimal":[48],"for":[50],"which":[51],"strata":[53],"are":[54],"homogeneous":[55],"given":[58,85,111],"constructible.":[61],"In":[62],"particular,":[63],"when":[64],"we":[65,122],"choose":[66],"to":[67,79,151],"work":[68],"local":[71,81],"homology":[72,82],"sheaf,":[73],"our":[74],"algorithm":[75,84,110],"gives":[76],"an":[77],"alternative":[78],"transfer":[83],"Bendich":[87],"et":[88,134],"al.":[89,135],"(Proceedings":[90],"23rd":[93],"Annual":[94],"ACM-SIAM":[95],"Symposium":[96],"Discrete":[98],"Algorithms,":[99],"pp.":[100],"1355\u20131370,":[101],"ACM,":[102],"New":[103],"York,":[104],"2012),":[105],"cohomology":[108],"Nanda":[113],"(Found.":[114],"Comput.":[115],"Math.":[116],"20":[117],"(2),":[118],"195\u2013222,":[119],"2020).":[120],"Additionally,":[121],"give":[123],"examples":[124],"stratifications":[126,153],"based":[127],"techniques":[131],"Breiding":[133],"(Rev.":[136],"Mat.":[137],"Complut.":[138],"31":[139],"(3),":[140],"545\u2013593,":[141],"2018),":[142],"illustrating":[143,178],"how":[144],"approach":[147,161],"can":[148],"be":[149],"used":[150],"study":[152,172],"both":[155],"This":[160],"also":[162],"points":[163],"toward":[164],"future":[165],"applications":[166],"theory":[169,186],"data":[175],"analysis":[176],"by":[177],"utility":[180],"language":[183],"generalizing":[188],"existing":[189],"algorithms.":[190]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}