{"id":"https://openalex.org/W4281710343","doi":"https://doi.org/10.48550/arxiv.2206.00606","title":"Topological Deep Learning: Going Beyond Graph Data","display_name":"Topological Deep Learning: Going Beyond Graph Data","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4281710343","doi":"https://doi.org/10.48550/arxiv.2206.00606"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2206.00606","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":["Cornell University"],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/2206.00606","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001225767","display_name":"Mustafa Hajij","orcid":"https://orcid.org/0000-0002-2625-9286"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hajij, Mustafa","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026457059","display_name":"Ghada Zamzmi","orcid":"https://orcid.org/0000-0003-4723-5539"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zamzmi, Ghada","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080301618","display_name":"Theodore Papamarkou","orcid":"https://orcid.org/0000-0002-9689-543X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Papamarkou, Theodore","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083733004","display_name":"Nina Miolane","orcid":"https://orcid.org/0000-0002-1200-9024"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miolane, Nina","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088677129","display_name":"Aldo Guzm\u00e1n-S\u00e1enz","orcid":"https://orcid.org/0000-0003-2725-621X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guzm\u00e1n-S\u00e1enz, Aldo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081874896","display_name":"Karthikeyan Natesan Ramamurthy","orcid":"https://orcid.org/0000-0002-6021-5930"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ramamurthy, Karthikeyan Natesan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038619214","display_name":"Tolga Birdal","orcid":"https://orcid.org/0000-0001-7915-7964"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Birdal, Tolga","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025354167","display_name":"Tamal K. Dey","orcid":"https://orcid.org/0000-0001-5160-9738"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dey, Tamal K.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052231787","display_name":"Soham Mukherjee","orcid":"https://orcid.org/0000-0003-0486-7763"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mukherjee, Soham","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041294470","display_name":"Shreyas N. Samaga","orcid":"https://orcid.org/0000-0002-4128-3946"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Samaga, Shreyas N.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050617364","display_name":"Neal Livesay","orcid":"https://orcid.org/0000-0003-4388-9850"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Livesay, Neal","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063254454","display_name":"Robin Walters","orcid":"https://orcid.org/0000-0002-9179-0321"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Walters, Robin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036159118","display_name":"Paul Rosen","orcid":"https://orcid.org/0000-0002-0873-9518"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rosen, Paul","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008584000","display_name":"Michael T. Schaub","orcid":"https://orcid.org/0000-0003-2426-6404"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schaub, Michael T.","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.99973,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9977,"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":0.9977,"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":0.9886,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.971,"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":[],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.53889906},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5306123},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4208169},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4079439},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34433383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28287786},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16419148}],"mesh":[],"locations_count":3,"locations":[{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2206.00606","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":["Cornell University"],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2206.00606","pdf_url":"http://arxiv.org/pdf/2206.00606","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.2206.00606","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2206.00606","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":["Cornell University"],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4360585206","https://openalex.org/W4323565446","https://openalex.org/W4321369474","https://openalex.org/W4285208911","https://openalex.org/W4213079790","https://openalex.org/W3215138031","https://openalex.org/W3082895349","https://openalex.org/W3009238340","https://openalex.org/W2731899572","https://openalex.org/W2248239756"],"abstract_inverted_index":{"Topological":[0],"deep":[1,14,46,228,247],"learning":[2,15,47,229,248],"is":[3],"a":[4,44,51,67,166],"rapidly":[5],"growing":[6],"field":[7],"that":[8,55,82,141,219],"pertains":[9],"to":[10,88,112,149,209,226,233],"the":[11,96,105,143,202,234,240],"development":[12],"of":[13,70,80,98,107,128,145,169,187,204,242],"models":[16,230,249],"for":[17],"data":[18,53],"supported":[19],"on":[20,95,178,206],"topological":[21,59,71,150],"domains":[22,34],"such":[23],"as":[24,78,137,224],"simplicial":[25,116],"complexes,":[26,28,66,133],"cell":[27,118,132],"and":[29,117,124,131,157,161,184,189,192,213],"hypergraphs,":[30,89],"which":[31,134],"generalize":[32,123],"many":[33],"encountered":[35],"in":[36,115,197,250],"scientific":[37],"computations.":[38],"In":[39,100],"this":[40],"paper,":[41],"we":[42,62,164,200],"present":[43],"unifying":[45],"framework":[48],"built":[49],"upon":[50,154],"richer":[52],"structure":[54],"includes":[56],"widely":[57],"adopted":[58],"domains.":[60],"Specifically,":[61],"first":[63],"introduce":[64],"combinatorial":[65,90,102,121,155,160,171],"novel":[68],"type":[69],"domain.":[72],"Combinatorial":[73],"complexes":[74,91,103,122,156],"can":[75],"be":[76],"seen":[77],"generalizations":[79],"graphs":[81],"maintain":[83],"certain":[84],"desirable":[85],"properties.":[86],"Similar":[87],"impose":[92],"no":[93],"constraints":[94],"set":[97],"relations.":[99],"addition,":[101],"permit":[104],"construction":[106],"hierarchical":[108],"higher-order":[109,244],"relations,":[110],"analogous":[111],"those":[113],"found":[114],"complexes.":[119],"Thus,":[120],"combine":[125],"useful":[126],"traits":[127],"both":[129],"hypergraphs":[130],"have":[135,221],"emerged":[136],"two":[138],"promising":[139],"abstractions":[140],"facilitate":[142],"generalization":[144],"graph":[146,214],"neural":[147,173],"networks":[148,174],"spaces.":[151],"Second,":[152],"building":[153],"their":[158],"rich":[159],"algebraic":[162],"structure,":[163],"develop":[165],"general":[167],"class":[168],"message-passing":[170],"complex":[172],"(CCNNs),":[175],"focusing":[176],"primarily":[177],"attention-based":[179],"CCNNs.":[180],"We":[181],"characterize":[182],"permutation":[183],"orientation":[185],"equivariances":[186],"CCNNs,":[188],"discuss":[190],"pooling":[191],"unpooling":[193],"operations":[194],"within":[195],"CCNNs":[196,205,220],"detail.":[198],"Third,":[199],"evaluate":[201],"performance":[203,223],"tasks":[207],"related":[208],"mesh":[210],"shape":[211],"analysis":[212],"learning.":[215],"Our":[216,237],"experiments":[217],"demonstrate":[218,239],"competitive":[222],"compared":[225],"state-of-the-art":[227],"specifically":[231],"tailored":[232],"same":[235],"tasks.":[236],"findings":[238],"advantages":[241],"incorporating":[243],"relations":[245],"into":[246],"different":[251],"applications.":[252]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4281710343","counts_by_year":[{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2024-12-07T18:04:17.256868","created_date":"2022-06-13"}