{"id":"https://openalex.org/W4417427637","doi":"https://doi.org/10.1109/tvcg.2025.3644671","title":"Topological Autoencoders++: Fast and Accurate Cycle-Aware Dimensionality Reduction","display_name":"Topological Autoencoders++: Fast and Accurate Cycle-Aware Dimensionality Reduction","publication_year":2025,"publication_date":"2025-12-15","ids":{"openalex":"https://openalex.org/W4417427637","doi":"https://doi.org/10.1109/tvcg.2025.3644671","pmid":"https://pubmed.ncbi.nlm.nih.gov/41396759"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2025.3644671","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2025.3644671","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":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-05004858","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092191570","display_name":"Matt\u00e9o Cl\u00e9mot","orcid":"https://orcid.org/0009-0000-2524-0244"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Matt\u00e9o Cl\u00e9mot","raw_affiliation_strings":["University Claude Bernard Lyon 1, Villeurbanne, France"],"raw_orcid":"https://orcid.org/0009-0000-2524-0244","affiliations":[{"raw_affiliation_string":"University Claude Bernard Lyon 1, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003311308","display_name":"Julie Digne","orcid":"https://orcid.org/0000-0003-0905-0840"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Julie Digne","raw_affiliation_strings":["CNRS, Paris, France"],"raw_orcid":"https://orcid.org/0000-0003-0905-0840","affiliations":[{"raw_affiliation_string":"CNRS, Paris, France","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"last","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":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Julien Tierny","raw_affiliation_strings":["CNRS, Paris, France"],"raw_orcid":"https://orcid.org/0000-0003-0056-2831","affiliations":[{"raw_affiliation_string":"CNRS, Paris, France","institution_ids":["https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5092191570"],"corresponding_institution_ids":["https://openalex.org/I100532134"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.37205387,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"2","first_page":"1622","last_page":"1639"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9973999857902527,"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":0.9973999857902527,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.00019999999494757503,"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/persistent-homology","display_name":"Persistent homology","score":0.8988000154495239},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"Topological data analysis","score":0.7278000116348267},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7099999785423279},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6101999878883362},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.605400025844574},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5965999960899353},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5336999893188477},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.4602999985218048}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.8988000154495239},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.7278000116348267},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7099999785423279},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6248999834060669},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6101999878883362},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.605400025844574},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5965999960899353},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5336999893188477},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.4602999985218048},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45100000500679016},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4187999963760376},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.4138999879360199},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3255999982357025},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C181576044","wikidata":"https://www.wikidata.org/wiki/Q4129926","display_name":"Computational topology","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2863999903202057},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C108882727","wikidata":"https://www.wikidata.org/wiki/Q2991685","display_name":"Solid modeling","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tvcg.2025.3644671","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2025.3644671","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:41396759","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41396759","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:HAL:hal-05004858v2","is_oa":true,"landing_page_url":"https://hal.science/hal-05004858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics, 2026, 32 (2), pp.1622-1639. ⟨10.1109/TVCG.2025.3644671⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-05004858v2","is_oa":true,"landing_page_url":"https://hal.science/hal-05004858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics, 2026, 32 (2), pp.1622-1639. ⟨10.1109/TVCG.2025.3644671⟩","raw_type":"Journal articles"},"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":62,"referenced_works":["https://openalex.org/W28435248","https://openalex.org/W1742512077","https://openalex.org/W1920826835","https://openalex.org/W1927021626","https://openalex.org/W1930589737","https://openalex.org/W1968721698","https://openalex.org/W1983948426","https://openalex.org/W1993436046","https://openalex.org/W1997780235","https://openalex.org/W2001141328","https://openalex.org/W2009940349","https://openalex.org/W2018701348","https://openalex.org/W2021845192","https://openalex.org/W2031973565","https://openalex.org/W2043508111","https://openalex.org/W2051574917","https://openalex.org/W2053186076","https://openalex.org/W2057869046","https://openalex.org/W2063295648","https://openalex.org/W2067049088","https://openalex.org/W2070784608","https://openalex.org/W2073197765","https://openalex.org/W2077572687","https://openalex.org/W2096510084","https://openalex.org/W2100495367","https://openalex.org/W2131493622","https://openalex.org/W2136630673","https://openalex.org/W2144968255","https://openalex.org/W2145347746","https://openalex.org/W2147408215","https://openalex.org/W2149203023","https://openalex.org/W2150372924","https://openalex.org/W2157514509","https://openalex.org/W2162825485","https://openalex.org/W2167963400","https://openalex.org/W2294510945","https://openalex.org/W2294798173","https://openalex.org/W2333586270","https://openalex.org/W2475195788","https://openalex.org/W2614596590","https://openalex.org/W2753153359","https://openalex.org/W2789480745","https://openalex.org/W2792823369","https://openalex.org/W2807795618","https://openalex.org/W2892037701","https://openalex.org/W2914594774","https://openalex.org/W2927507212","https://openalex.org/W2951435719","https://openalex.org/W2964534207","https://openalex.org/W2997113231","https://openalex.org/W2997591727","https://openalex.org/W3013843370","https://openalex.org/W3023779798","https://openalex.org/W3090266290","https://openalex.org/W3198723315","https://openalex.org/W3202868818","https://openalex.org/W4205380271","https://openalex.org/W4255383393","https://openalex.org/W4289688996","https://openalex.org/W4313421805","https://openalex.org/W4317532093","https://openalex.org/W4402402059"],"related_works":[],"abstract_inverted_index":{"This":[0,128],"paper":[1],"presents":[2],"a":[3,39,50,76,87,103,138,168,196],"novel":[4,40,104],"topology-aware":[5,190],"dimensionality":[6],"reduction":[7],"approach":[8],"aiming":[9],"at":[10],"accurately":[11],"visualizing":[12],"the":[13,27,64,70,116,124,133,147,160,163,173,182,200,206,210,214],"cyclic":[14],"patterns":[15],"present":[16],"in":[17,154,162,181,216],"high":[18,59],"dimensional":[19],"data.":[20],"To":[21],"that":[22,49,80],"end,":[23],"we":[24,37,101],"build":[25],"on":[26,98,132],"Topological":[28],"Autoencoders":[29],"(TopoAE)":[30],"(Moor":[31],"et":[32],"al.,":[33],"2020)":[34],"formulation.":[35],"First,":[36],"provide":[38,75],"theoretical":[41],"analysis":[42],"of":[43,69,90,106,119,135,146,159,176,213],"its":[44],"associated":[45],"loss":[46,52],"and":[47,60,209],"show":[48],"zero":[51],"indeed":[53],"induces":[54],"identical":[55],"persistence":[56],"pairs":[57],"(in":[58],"low":[61,217],"dimensions)":[62],"for":[63,86,94,115,172,178],"0-dimensional":[65],"persistent":[66,110,150],"homology":[67,111],"($\\text{PH}^{0}$)":[68],"Rips":[71,179],"filtration.":[72],"We":[73,165],"also":[74,194],"counter":[77],"example":[78],"showing":[79],"this":[81,99],"property":[82],"no":[83],"longer":[84],"holds":[85],"naive":[88],"extension":[89],"TopoAE":[91,107],"to":[92,108],"$\\text{PH}^{d}$":[93],"$d\\geq":[95],"1$.":[96],"Based":[97],"observation,":[100],"introduce":[102,167],"generalization":[105,129],"1-dimensional":[109],"($\\text{PH}^{1}$),":[112],"called":[113],"TopoAE++,":[114],"accurate":[117],"generation":[118],"cycle-aware":[120],"planar":[121],"embeddings,":[122],"addressing":[123],"above":[125],"failure":[126],"case.":[127],"is":[130],"based":[131],"notion":[134],"cascade":[136],"distortion,":[137],"new":[139],"penalty":[140],"term":[141],"favoring":[142],"an":[143],"isometric":[144],"embedding":[145],"2-chains":[148],"filling":[149],"1-cycles,":[151],"hence":[152],"resulting":[153],"more":[155],"faithful":[156],"geometrical":[157],"reconstructions":[158],"1-cycles":[161],"plane.":[164],"further":[166],"novel,":[169],"fast":[170],"algorithm":[171],"exact":[174],"computation":[175],"$\\text{PH}^{}$":[177],"filtrations":[180],"plane,":[183],"yielding":[184],"improved":[185],"runtimes":[186],"over":[187],"previously":[188],"documented":[189],"methods.":[191],"Our":[192],"method":[193],"achieves":[195],"better":[197],"balance":[198],"between":[199],"topological":[201],"accuracy,":[202],"as":[203],"measured":[204],"by":[205],"Wasserstein":[207],"distance,":[208],"visual":[211],"preservation":[212],"cycles":[215],"dimensions.":[218]},"counts_by_year":[],"updated_date":"2026-05-15T08:27:34.491423","created_date":"2025-12-15T00:00:00"}