{"id":"https://openalex.org/W3174966384","doi":"https://doi.org/10.1109/tpami.2021.3091682","title":"Signed Graph Metric Learning via Gershgorin Disc Perfect Alignment","display_name":"Signed Graph Metric Learning via Gershgorin Disc Perfect Alignment","publication_year":2021,"publication_date":"2021-06-23","ids":{"openalex":"https://openalex.org/W3174966384","doi":"https://doi.org/10.1109/tpami.2021.3091682","mag":"3174966384","pmid":"https://pubmed.ncbi.nlm.nih.gov/34161237"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2021.3091682","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3091682","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,"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"},"type":"article","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/A5075921874","display_name":"Cheng Yang","orcid":"https://orcid.org/0000-0002-3540-1598"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cheng Yang","raw_affiliation_strings":["Shanghai Jiao Tong University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038897476","display_name":"Gene Cheung","orcid":"https://orcid.org/0000-0002-5571-4137"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Gene Cheung","raw_affiliation_strings":["York University, Toronto, ON, Canada"],"affiliations":[{"raw_affiliation_string":"York University, Toronto, ON, Canada","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059045087","display_name":"Wei Hu","orcid":"https://orcid.org/0000-0002-9860-0922"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Hu","raw_affiliation_strings":["Peking University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5075921874"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":2.0174,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.88624183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"44","issue":"10","first_page":"7219","last_page":"7234"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9952999949455261,"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"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9952999949455261,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9855999946594238,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6481351852416992},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5014216899871826},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4937232434749603},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.48345670104026794},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4315507411956787},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.4302331507205963},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.41416722536087036},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39048266410827637},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3534497916698456},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07944366335868835}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6481351852416992},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5014216899871826},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4937232434749603},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.48345670104026794},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4315507411956787},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.4302331507205963},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.41416722536087036},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39048266410827637},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3534497916698456},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07944366335868835},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2021.3091682","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3091682","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,"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:34161237","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34161237","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 pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6499999761581421,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[{"id":"https://openalex.org/G3604809996","display_name":null,"funder_award_id":"61972009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4251215508","display_name":null,"funder_award_id":"RGPAS-2019-00110","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G854496103","display_name":null,"funder_award_id":"2020TQ0194","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G968945561","display_name":null,"funder_award_id":"RGPIN-2019-06271","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W117710940","https://openalex.org/W658512522","https://openalex.org/W1511572470","https://openalex.org/W1905908634","https://openalex.org/W1975517671","https://openalex.org/W2042353152","https://openalex.org/W2051142108","https://openalex.org/W2076434944","https://openalex.org/W2096733369","https://openalex.org/W2106053110","https://openalex.org/W2110654099","https://openalex.org/W2114051435","https://openalex.org/W2118840614","https://openalex.org/W2124608575","https://openalex.org/W2132555912","https://openalex.org/W2136261952","https://openalex.org/W2138621090","https://openalex.org/W2142517301","https://openalex.org/W2145287260","https://openalex.org/W2150796457","https://openalex.org/W2564596500","https://openalex.org/W2571662414","https://openalex.org/W2605052559","https://openalex.org/W2623293810","https://openalex.org/W2767325013","https://openalex.org/W2796431263","https://openalex.org/W2894849414","https://openalex.org/W2900169675","https://openalex.org/W2961495769","https://openalex.org/W2962978500","https://openalex.org/W2963026027","https://openalex.org/W2963026686","https://openalex.org/W2963302943","https://openalex.org/W2963775347","https://openalex.org/W2964228184","https://openalex.org/W3015921871","https://openalex.org/W3142000089","https://openalex.org/W4211015501","https://openalex.org/W4213376838","https://openalex.org/W4221135977","https://openalex.org/W4229706427","https://openalex.org/W4230938240","https://openalex.org/W4241368925","https://openalex.org/W4244393449","https://openalex.org/W4250589301","https://openalex.org/W4312258136","https://openalex.org/W6600043445","https://openalex.org/W6632267817","https://openalex.org/W6632543029","https://openalex.org/W6675655370","https://openalex.org/W6675751002","https://openalex.org/W6676757673","https://openalex.org/W6677328822","https://openalex.org/W6677884823","https://openalex.org/W6681239517","https://openalex.org/W6719959352"],"related_works":["https://openalex.org/W1529195008","https://openalex.org/W2034395027","https://openalex.org/W2028994362","https://openalex.org/W4384918718","https://openalex.org/W38983538","https://openalex.org/W2924468784","https://openalex.org/W2034598826","https://openalex.org/W4285317199","https://openalex.org/W2990914270","https://openalex.org/W2087913063"],"abstract_inverted_index":{"Given":[0],"a":[1,8,24,41,63,82],"convex":[2],"and":[3,92,108,116,223],"differentiable":[4],"objective":[5],"Q(M)":[6],"for":[7],"real":[9],"symmetric":[10],"matrix":[11,96,110],"M":[12,38,54,105,177,206],"in":[13,40,72,153,176,205],"the":[14,73,77,119,140,149,154,167,171,186],"positive":[15],"definite":[16],"(PD)":[17],"cone-used":[18],"to":[19,50,88],"compute":[20],"Mahalanobis":[21],"distances-we":[22],"propose":[23],"fast":[25,94],"general":[26],"metric":[27,65,69,95,155,215],"learning":[28,156],"framework":[29],"that":[30,37,57,126,166,212],"is":[31,58,61,98,118,217],"entirely":[32],"projection-free.":[33],"We":[34,189],"first":[35,120],"assume":[36],"resides":[39],"space":[42],"S":[43,56,75,107],"of":[44,122,130,170],"generalized":[45],"graph":[46,64,214],"Laplacian":[47],"matrices":[48,70,80],"corresponding":[49],"balanced":[51],"signed":[52],"graphs.":[53],"\u2208":[55,106],"also":[59],"PD":[60,150],"called":[62],"matrix.":[66],"Unlike":[67],"low-rank":[68],"common":[71],"literature,":[74],"includes":[76],"important":[78],"diagonal-only":[79],"as":[81,182,203],"special":[83],"case.":[84],"The":[85],"key":[86],"theorem":[87],"circumvent":[89],"full":[90],"eigen-decomposition":[91],"enable":[93],"optimization":[97,169,216],"Gershgorin":[99,127],"disc":[100,128],"perfect":[101],"alignment":[102],"(GDPA):":[103],"given":[104],"diagonal":[109,172],"S,":[111],"where":[112],"S<sub>ii</sub>":[113],"=":[114,134],"1/v<sub>i</sub>":[115],"v":[117,191],"eigenvector":[121],"M,":[123],"we":[124,147],"prove":[125],"left-ends":[129],"similarity":[131],"transform":[132],"B":[133],"SMS<sup>-1</sup>":[135],"are":[136,207],"perfectly":[137],"aligned":[138],"at":[139],"smallest":[141],"eigenvalue":[142],"\u03bb<sub>min</sub>.":[143],"Using":[144],"this":[145],"theorem,":[146],"replace":[148],"cone":[151],"constraint":[152],"problem":[157],"with":[158,200],"tightest":[159],"possible":[160],"linear":[161,183],"constraints":[162],"per":[163],"iteration,":[164],"so":[165],"alternating":[168],"/":[173],"off-diagonal":[174],"terms":[175],"can":[178],"be":[179],"solved":[180],"efficiently":[181],"programs":[184],"via":[185],"Frank-Wolfe":[187],"method.":[188],"update":[190],"using":[192],"Locally":[193],"Optimal":[194],"Block":[195],"Preconditioned":[196],"Conjugate":[197],"Gradient":[198],"(LOBPCG)":[199],"warm":[201],"start":[202],"entries":[204],"optimized":[208],"successively.":[209],"Experiments":[210],"show":[211],"our":[213],"significantly":[218],"faster":[219],"than":[220],"cone-projection":[221],"schemes,":[222],"produces":[224],"competitive":[225],"binary":[226],"classification":[227],"performance.":[228]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
