{"id":"https://openalex.org/W7204581435","doi":"https://doi.org/10.1109/tpami.2026.3726957","title":"Multi-View Spectral Contrastive Learning","display_name":"Multi-View Spectral Contrastive Learning","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7204581435","doi":"https://doi.org/10.1109/tpami.2026.3726957","pmid":"https://pubmed.ncbi.nlm.nih.gov/42664107"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2026.3726957","doi":"https://doi.org/10.1109/tpami.2026.3726957","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2026.3726957","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["ccf-a","cwts-core","dongbi-a","doyens","jufo-3","medline","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"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/A5060079967","display_name":"Bing Cai","orcid":"https://orcid.org/0000-0002-2360-2579","observed_orcids":["https://orcid.org/0000-0002-2360-2579"]},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bing Cai","raw_affiliation_strings":["Nanjing University of Science and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanjing University of Science and Technology","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100456916","display_name":"Xiaoli Wang","orcid":"https://orcid.org/0000-0002-9388-0734","observed_orcids":["https://orcid.org/0000-0002-9388-0734"]},"institutions":[{"id":"https://openalex.org/I167027274","display_name":"Nanjing Forestry University","ror":"https://ror.org/03m96p165","country_code":"CN","type":"education","lineage":["https://openalex.org/I167027274"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoli Wang","raw_affiliation_strings":["Nanjing Forestry University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanjing Forestry University","institution_ids":["https://openalex.org/I167027274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043127950","display_name":"Gui\u2010Fu Lu","orcid":"https://orcid.org/0000-0001-9047-6579","observed_orcids":["https://orcid.org/0000-0001-9047-6579","https://orcid.org/0000-0002-1897-6154"]},"institutions":[{"id":"https://openalex.org/I70908550","display_name":"Anhui Polytechnic University","ror":"https://ror.org/041sj0284","country_code":"CN","type":"education","lineage":["https://openalex.org/I70908550"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gui-Fu Lu","raw_affiliation_strings":["Anhui Polytechnic University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Anhui Polytechnic University","institution_ids":["https://openalex.org/I70908550"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017096005","display_name":"Zechao Li","orcid":"https://orcid.org/0000-0002-5341-5985","observed_orcids":["https://orcid.org/0000-0002-5341-5985","https://orcid.org/0000-0001-5698-6022"]},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zechao Li","raw_affiliation_strings":["Nanjing University of Science and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanjing University of Science and Technology","institution_ids":["https://openalex.org/I36399199"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.55113841,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"PP","issue":null,"first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.7904999852180481,"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"}},"topics":[{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.7904999852180481,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.11760000139474869,"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/T10057","display_name":"Face and Expression Recognition","score":0.05389999970793724,"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/multi-view-learning","display_name":"multi-view learning","score":0.7820000052452087},{"id":"https://openalex.org/keywords/spectral-clustering","display_name":"spectral clustering","score":0.8479999899864197},{"id":"https://openalex.org/keywords/contrastive-learning","display_name":"contrastive learning","score":0.9769999980926514},{"id":"https://openalex.org/keywords/graph-laplacian","display_name":"graph Laplacian","score":0.7900000214576721},{"id":"https://openalex.org/keywords/spectral-embedding","display_name":"spectral embedding","score":0.7110000252723694},{"id":"https://openalex.org/keywords/orthogonality-constraints","display_name":"orthogonality constraints","score":0.8169999718666077},{"id":"https://openalex.org/keywords/laplacian-smoothing","display_name":"Laplacian smoothing","score":0.8759999871253967},{"id":"https://openalex.org/keywords/multi-view-clustering","display_name":"multi-view clustering","score":0.6759999990463257}],"concepts":[{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.739799976348877},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6452999711036682},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5275999903678894},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.525600016117096},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.5238999724388123},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5164999961853027},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5069000124931335},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.44269999861717224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4000000059604645},{"id":"https://openalex.org/C2776879701","wikidata":"https://www.wikidata.org/wiki/Q25048660","display_name":"Multiple kernel learning","level":4,"score":0.39309999346733093},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3919000029563904},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3619999885559082},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.27630001306533813},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.27079999446868896},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2623000144958496},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.25870001316070557},{"id":"https://openalex.org/C54926389","wikidata":"https://www.wikidata.org/wiki/Q7575188","display_name":"Spectral envelope","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2026.3726957","doi":"https://doi.org/10.1109/tpami.2026.3726957","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2026.3726957","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["ccf-a","cwts-core","dongbi-a","doyens","jufo-3","medline","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:42664107","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42664107","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,"listed_in":[],"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 pattern analysis and machine intelligence","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4388071281","https://openalex.org/W4281722953","https://openalex.org/W2965624713","https://openalex.org/W4310595044","https://openalex.org/W4385262341","https://openalex.org/W4386798129","https://openalex.org/W4403600933","https://openalex.org/W4317568990","https://openalex.org/W2518130590","https://openalex.org/W2964368963"],"abstract_inverted_index":{"Spectral":[0,47],"clustering":[1,61,113,175],"provides":[2],"a":[3,51,63,75,81,98,148,153],"principled":[4,34,154],"framework":[5,54],"for":[6,36,104],"partitioning":[7],"data":[8],"through":[9],"graph":[10],"Laplacian":[11,145],"optimization,":[12],"yet":[13],"its":[14,188],"integration":[15],"into":[16,110],"deep":[17,111],"multi-view":[18,174],"learning":[19,58,158],"remains":[20],"fundamentally":[21],"challenging":[22],"due":[23],"to":[24,85,114,125],"hard":[25,116],"orthogonality":[26,117],"constraints,":[27],"numerical":[28],"instability,":[29],"and":[30,59,79,129,159,183,190],"the":[31,89,105,137],"lack":[32],"of":[33,95],"mechanisms":[35],"fusing":[37],"multiple":[38,69],"spectral":[39,60,71,77,82,90,112,160],"operators.":[40],"In":[41],"this":[42],"paper,":[43],"we":[44],"propose":[45],"Multi-View":[46],"Contrastive":[48],"Learning":[49],"(MSCL),":[50],"theoretically":[52],"grounded":[53],"that":[55,136,169],"unifies":[56],"contrastive":[57,83,139,157],"from":[62],"spectral-operator":[64],"perspective.":[65],"MSCL":[66,96,170],"jointly":[67],"optimizes":[68],"view-specific":[70],"embeddings":[72],"together":[73],"with":[74],"consensus":[76],"embedding,":[78],"introduces":[80],"regularization":[84],"align":[86],"them":[87],"in":[88],"domain.":[91],"A":[92],"key":[93],"component":[94],"is":[97,108],"differentiable":[99],"Newton-Schulz":[100],"orthogonalization":[101,181],"module,":[102],"which,":[103],"first":[106],"time,":[107],"introduced":[109],"enforce":[115],"without":[118],"explicit":[119],"matrix":[120],"decomposition":[121],"or":[122],"inversion,":[123],"leading":[124],"numerically":[126],"stable":[127],"optimization":[128],"smooth":[130],"gradient":[131],"propagation.":[132],"We":[133],"further":[134,186],"show":[135],"proposed":[138],"loss":[140],"admits":[141],"an":[142],"interpretation":[143],"as":[144],"smoothing":[146],"on":[147,164,180],"kernel-induced":[149],"similarity":[150],"graph,":[151],"establishing":[152],"connection":[155],"between":[156],"optimization.":[161],"Extensive":[162],"experiments":[163],"twelve":[165],"benchmark":[166],"datasets":[167],"demonstrate":[168],"consistently":[171],"outperforms":[172],"state-of-the-art":[173],"methods,":[176],"while":[177],"additional":[178],"analyses":[179],"stability":[182],"kernel":[184],"choice":[185],"validate":[187],"robustness":[189],"scalability.":[191]},"counts_by_year":[],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2026-08-29T00:00:00"}