{"id":"https://openalex.org/W3082778322","doi":"https://doi.org/10.1109/tvcg.2020.3030441","title":"TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data","display_name":"TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data","publication_year":2020,"publication_date":"2020-10-13","ids":{"openalex":"https://openalex.org/W3082778322","doi":"https://doi.org/10.1109/tvcg.2020.3030441","mag":"3082778322","pmid":"https://pubmed.ncbi.nlm.nih.gov/33048736"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2020.3030441","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2020.3030441","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2009.01512","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033801646","display_name":"Harish Doraiswamy","orcid":"https://orcid.org/0000-0003-2995-250X"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Harish Doraiswamy","raw_affiliation_strings":["New York University"],"affiliations":[{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074734666","display_name":"Julien Tierny","orcid":"https://orcid.org/0000-0003-0056-2831"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Julien Tierny","raw_affiliation_strings":["CNRS and Sorbonne Universit\u00e9","[CNRS and Sorbonne Universit\u00e9]"],"affiliations":[{"raw_affiliation_string":"CNRS and Sorbonne Universit\u00e9","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"[CNRS and Sorbonne Universit\u00e9]","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033833921","display_name":"Paulo J. S. Silva","orcid":"https://orcid.org/0000-0003-1340-965X"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Paulo J. S. Silva","raw_affiliation_strings":["University of Campinas"],"affiliations":[{"raw_affiliation_string":"University of Campinas","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011424640","display_name":"Lu\u00eds Gustavo Nonato","orcid":"https://orcid.org/0000-0002-8514-8033"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Luis Gustavo Nonato","raw_affiliation_strings":["University of Sao Paulo, Sao Carlos","University of São Paulo, São Carlos"],"affiliations":[{"raw_affiliation_string":"University of Sao Paulo, Sao Carlos","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"University of São Paulo, São Carlos","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052577630","display_name":"Cl\u00e1udio Silva","orcid":"https://orcid.org/0000-0002-5831-2993"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Claudio Silva","raw_affiliation_strings":["New York University"],"affiliations":[{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5033801646"],"corresponding_institution_ids":["https://openalex.org/I57206974"],"apc_list":null,"apc_paid":null,"fwci":0.578,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73788151,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"27","issue":"2","first_page":"561","last_page":"571"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9664999842643738,"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":0.9664999842643738,"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/T10799","display_name":"Data Visualization and Analytics","score":0.024900000542402267,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.0035000001080334187,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/projection","display_name":"Projection (relational algebra)","score":0.5292524695396423},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5149139165878296},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.486333429813385},{"id":"https://openalex.org/keywords/computational-biology","display_name":"Computational biology","score":0.3885849714279175},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32615992426872253},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.24638494849205017},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.2029394507408142},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15332061052322388}],"concepts":[{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5292524695396423},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5149139165878296},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.486333429813385},{"id":"https://openalex.org/C70721500","wikidata":"https://www.wikidata.org/wiki/Q177005","display_name":"Computational biology","level":1,"score":0.3885849714279175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32615992426872253},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.24638494849205017},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.2029394507408142},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15332061052322388},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tvcg.2020.3030441","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2020.3030441","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},{"id":"pmid:33048736","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33048736","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on visualization and computer graphics","raw_type":null},{"id":"pmh:oai:arXiv.org:2009.01512","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.01512","pdf_url":"https://arxiv.org/pdf/2009.01512","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"},{"id":"pmh:oai:HAL:hal-02949185v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02949185","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics, 2020","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.2009.01512","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2009.01512","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2009.01512","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.01512","pdf_url":"https://arxiv.org/pdf/2009.01512","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G465780485","display_name":null,"funder_award_id":"ERC-2019-COG","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":82,"referenced_works":["https://openalex.org/W28435248","https://openalex.org/W107886322","https://openalex.org/W1513214262","https://openalex.org/W1582500501","https://openalex.org/W1600748172","https://openalex.org/W1607787316","https://openalex.org/W1654438081","https://openalex.org/W1716233801","https://openalex.org/W1742512077","https://openalex.org/W1920826835","https://openalex.org/W1927021626","https://openalex.org/W1930589737","https://openalex.org/W1957046493","https://openalex.org/W1967994289","https://openalex.org/W1970754929","https://openalex.org/W1983948426","https://openalex.org/W1987995897","https://openalex.org/W1991566301","https://openalex.org/W2001141328","https://openalex.org/W2001887552","https://openalex.org/W2008581147","https://openalex.org/W2018701348","https://openalex.org/W2021845192","https://openalex.org/W2030347560","https://openalex.org/W2030991373","https://openalex.org/W2037613900","https://openalex.org/W2051574917","https://openalex.org/W2053186076","https://openalex.org/W2055061536","https://openalex.org/W2067298033","https://openalex.org/W2070784608","https://openalex.org/W2076137473","https://openalex.org/W2079272025","https://openalex.org/W2088323702","https://openalex.org/W2096510084","https://openalex.org/W2129904086","https://openalex.org/W2131493622","https://openalex.org/W2135830218","https://openalex.org/W2137570937","https://openalex.org/W2144968255","https://openalex.org/W2145347746","https://openalex.org/W2147408215","https://openalex.org/W2150372924","https://openalex.org/W2153504150","https://openalex.org/W2153934661","https://openalex.org/W2155865164","https://openalex.org/W2156287497","https://openalex.org/W2157514509","https://openalex.org/W2157701289","https://openalex.org/W2162825485","https://openalex.org/W2167963400","https://openalex.org/W2187089797","https://openalex.org/W2187483593","https://openalex.org/W2271464269","https://openalex.org/W2475195788","https://openalex.org/W2517066960","https://openalex.org/W2592128618","https://openalex.org/W2614596590","https://openalex.org/W2620795156","https://openalex.org/W2753153359","https://openalex.org/W2760469934","https://openalex.org/W2786672974","https://openalex.org/W2789480745","https://openalex.org/W2807795618","https://openalex.org/W2808728085","https://openalex.org/W2892037701","https://openalex.org/W2994761520","https://openalex.org/W2997113231","https://openalex.org/W3013843370","https://openalex.org/W3104206703","https://openalex.org/W3120740533","https://openalex.org/W3145128584","https://openalex.org/W3175762873","https://openalex.org/W4205380271","https://openalex.org/W6636338475","https://openalex.org/W6636879311","https://openalex.org/W6637681452","https://openalex.org/W6682757982","https://openalex.org/W6683047094","https://openalex.org/W6739097744","https://openalex.org/W6748816842","https://openalex.org/W6751833036"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2130043461","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Multidimensional":[0],"Projection":[1],"is":[2],"a":[3,24,28,97,137,158,162],"fundamental":[4],"tool":[5],"for":[6,44],"high-dimensional":[7,25,159,177],"data":[8,22,82],"analytics":[9],"and":[10,109,131],"visualization.":[11],"With":[12],"very":[13],"few":[14],"exceptions,":[15],"projection":[16,63,139,231],"techniques":[17],"are":[18,87],"designed":[19,53],"to":[20,27,33,54,66,93,124,161,190,214,224],"map":[21],"from":[23,157],"space":[26,30,160],"visual":[29,163,216],"so":[31],"as":[32,40,75,107,123,128,193,195],"preserve":[34,67],"some":[35,121],"dissimilarity":[36,68],"(similarity)":[37],"measure,":[38],"such":[39,74,106,127],"the":[41,59,78,89,101,117,146,151,155,167,172,176,181,184,191,204,215,227],"Euclidean":[42],"distance":[43],"example.":[45],"In":[46,149],"fact,":[47],"although":[48],"adopting":[49],"distinct":[50],"mathematical":[51],"formulations":[52],"favor":[55],"different":[56],"aspects":[57],"of":[58,103,171,175,229],"data,":[60,178],"most":[61],"multidimensional":[62],"methods":[64],"strive":[65],"measures":[69],"that":[70,180,203],"encapsulate":[71],"geometric":[72,85],"properties":[73],"distances":[76],"or":[77],"proximity":[79],"relation":[80],"between":[81],"objects.":[83],"However,":[84],"relations":[86],"not":[88,210],"only":[90,211],"interesting":[91],"property":[92],"be":[94,112,222],"preserved":[95],"in":[96,226],"projection.":[98],"For":[99],"instance,":[100],"analysis":[102],"particular":[104],"structures":[105],"clusters":[108],"outliers":[110],"could":[111],"more":[113],"reliably":[114],"performed":[115],"if":[116],"mapping":[118,147,156],"process":[119,218],"gives":[120],"guarantee":[122,206],"topological":[125,143,205],"invariants":[126],"connected":[129,186],"components":[130,187],"loops.":[132],"This":[133],"paper":[134],"introduces":[135],"TopoMap,":[136],"novel":[138],"technique":[140],"which":[141],"provides":[142],"guarantees":[144],"during":[145],"process.":[148],"particular,":[150],"proposed":[152],"method":[153],"performs":[154],"space,":[164],"while":[165],"preserving":[166],"0-dimensional":[168],"persistence":[169],"diagram":[170],"Rips":[173],"filtration":[174],"ensuring":[179],"filtrations":[182],"generate":[183],"same":[185],"when":[188],"applied":[189],"original":[192],"well":[194],"projected":[196],"data.":[197],"The":[198],"presented":[199],"case":[200],"studies":[201],"show":[202],"provided":[207],"by":[208],"TopoMap":[209],"brings":[212],"confidence":[213],"analytic":[217],"but":[219],"also":[220],"can":[221],"used":[223],"assist":[225],"assessment":[228],"other":[230],"methods.":[232]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}