{"id":"https://openalex.org/W3169679087","doi":"https://doi.org/10.1162/neco_a_01402","title":"Direction Matters: On Influence-Preserving Graph Summarization and Max-Cut Principle for Directed Graphs","display_name":"Direction Matters: On Influence-Preserving Graph Summarization and Max-Cut Principle for Directed Graphs","publication_year":2021,"publication_date":"2021-06-07","ids":{"openalex":"https://openalex.org/W3169679087","doi":"https://doi.org/10.1162/neco_a_01402","mag":"3169679087","pmid":"https://pubmed.ncbi.nlm.nih.gov/34310677"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_01402","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01402","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10138/338826","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101711249","display_name":"Wenkai Xu","orcid":"https://orcid.org/0000-0002-0073-8377"},"institutions":[{"id":"https://openalex.org/I4210115172","display_name":"Oxford Centre for Computational Neuroscience","ror":"https://ror.org/026ejyb70","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210115172"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Wenkai Xu","raw_affiliation_strings":["Gatsby Unit of Computational Neuroscience, London W1T 4JG, U.K. xwk4813@gmail.com"],"affiliations":[{"raw_affiliation_string":"Gatsby Unit of Computational Neuroscience, London W1T 4JG, U.K. xwk4813@gmail.com","institution_ids":["https://openalex.org/I4210115172"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101445444","display_name":"Gang Niu","orcid":"https://orcid.org/0000-0002-8652-239X"},"institutions":[{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Gang Niu","raw_affiliation_strings":["RIKEN Center for Advanced Intelligence Report, Tokyo 103-0027, Japan gang.niu@riken.jp"],"affiliations":[{"raw_affiliation_string":"RIKEN Center for Advanced Intelligence Report, Tokyo 103-0027, Japan gang.niu@riken.jp","institution_ids":["https://openalex.org/I4210126580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061498233","display_name":"Aapo Hyv\u00e4rinen","orcid":"https://orcid.org/0000-0002-5806-4432"},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"funder","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I4210128565","display_name":"CEA Paris-Saclay","ror":"https://ror.org/03n15ch10","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210128565"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]}],"countries":["FI","FR"],"is_corresponding":true,"raw_author_name":"Aapo Hyv\u00e4rinen","raw_affiliation_strings":["Universit\u00e9 Paris-Saclay, Inria, CEA, Paris 91120, France, and University of Helsinki, FIN00560 Helsinki, Finland aapo.hyvarinen@helsinki.fi"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay, Inria, CEA, Paris 91120, France, and University of Helsinki, FIN00560 Helsinki, Finland aapo.hyvarinen@helsinki.fi","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I277688954","https://openalex.org/I2738703131","https://openalex.org/I4210128565"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072744508","display_name":"Masashi Sugiyama","orcid":"https://orcid.org/0000-0001-6658-6743"},"institutions":[{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masashi Sugiyama","raw_affiliation_strings":["RIKEN, Center for Advanced Intelligence Report, Tokyo 103-0027, Japan, and University of Tokyo, Tokyo 113-0033, Japan sugi@k.u-tokyo.ac.jp"],"affiliations":[{"raw_affiliation_string":"RIKEN, Center for Advanced Intelligence Report, Tokyo 103-0027, Japan, and University of Tokyo, Tokyo 113-0033, Japan sugi@k.u-tokyo.ac.jp","institution_ids":["https://openalex.org/I4210126580","https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061498233","https://openalex.org/A5072744508","https://openalex.org/A5101445444","https://openalex.org/A5101711249"],"corresponding_institution_ids":["https://openalex.org/I133731052","https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210115172","https://openalex.org/I4210126580","https://openalex.org/I4210128565","https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":0.1298,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.4369396,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"33","issue":"8","first_page":"2128","last_page":"2162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9961000084877014,"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/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/automatic-summarization","display_name":"Automatic summarization","score":0.5309464335441589},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.5158840417861938},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.5116677284240723},{"id":"https://openalex.org/keywords/identifiability","display_name":"Identifiability","score":0.49593624472618103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4861466586589813},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.472042441368103},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4437289535999298},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4064823091030121},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3945843279361725},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3020811676979065},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.22013148665428162}],"concepts":[{"id":"https://openalex.org/C170858558","wikidata":"https://www.wikidata.org/wiki/Q1394144","display_name":"Automatic summarization","level":2,"score":0.5309464335441589},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.5158840417861938},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.5116677284240723},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.49593624472618103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4861466586589813},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.472042441368103},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4437289535999298},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4064823091030121},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3945843279361725},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3020811676979065},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.22013148665428162},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1162/neco_a_01402","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01402","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:34310677","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34310677","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":"Neural computation","raw_type":null},{"id":"pmh:oai:helda.helsinki.fi:10138/338826","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/338826","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:helda.helsinki.fi:10138/338826","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/338826","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W143174683","https://openalex.org/W155548076","https://openalex.org/W595331685","https://openalex.org/W1525315351","https://openalex.org/W1573318337","https://openalex.org/W1594662659","https://openalex.org/W1599627005","https://openalex.org/W1736023725","https://openalex.org/W1949719358","https://openalex.org/W1976387764","https://openalex.org/W1994219736","https://openalex.org/W2013912476","https://openalex.org/W2015583498","https://openalex.org/W2024165284","https://openalex.org/W2025603201","https://openalex.org/W2025624027","https://openalex.org/W2040491446","https://openalex.org/W2043545458","https://openalex.org/W2045512849","https://openalex.org/W2077491345","https://openalex.org/W2089554624","https://openalex.org/W2100132188","https://openalex.org/W2106474670","https://openalex.org/W2107559689","https://openalex.org/W2107709347","https://openalex.org/W2108781142","https://openalex.org/W2109603993","https://openalex.org/W2114977008","https://openalex.org/W2119741678","https://openalex.org/W2121947440","https://openalex.org/W2124066753","https://openalex.org/W2127048411","https://openalex.org/W2128859735","https://openalex.org/W2140986872","https://openalex.org/W2144920235","https://openalex.org/W2146008005","https://openalex.org/W2152430833","https://openalex.org/W2167299987","https://openalex.org/W2168103112","https://openalex.org/W2169343523","https://openalex.org/W2169876669","https://openalex.org/W2170902455","https://openalex.org/W2178789211","https://openalex.org/W2230451985","https://openalex.org/W2292193262","https://openalex.org/W2313049648","https://openalex.org/W2374597300","https://openalex.org/W2404400936","https://openalex.org/W2437552536","https://openalex.org/W2564453501","https://openalex.org/W2792990871","https://openalex.org/W2793963910","https://openalex.org/W2798766386","https://openalex.org/W2952490502","https://openalex.org/W2962936633","https://openalex.org/W2999905431","https://openalex.org/W3021064838","https://openalex.org/W3098742898","https://openalex.org/W3100362512","https://openalex.org/W3102641634","https://openalex.org/W3204446801","https://openalex.org/W4302322070","https://openalex.org/W4396738453","https://openalex.org/W6606275788","https://openalex.org/W6635799125","https://openalex.org/W6685245074","https://openalex.org/W6718111868"],"related_works":["https://openalex.org/W2724847603","https://openalex.org/W2034041141","https://openalex.org/W2366403280","https://openalex.org/W2184661725","https://openalex.org/W2900187352","https://openalex.org/W2573470972","https://openalex.org/W1495108544","https://openalex.org/W2105626102","https://openalex.org/W2131038454","https://openalex.org/W112856298"],"abstract_inverted_index":{"Summarizing":[0],"large-scale":[1],"directed":[2,39,64,141],"graphs":[3,93],"into":[4,30],"small-scale":[5,60],"representations":[6],"is":[7,154],"a":[8,36,55,63,117,130],"useful":[9,105],"but":[10],"less-studied":[11],"problem":[12],"setting.":[13],"Conventional":[14],"clustering":[15],"approaches,":[16],"based":[17,119],"on":[18,120,161],"Min-Cut-style":[19],"criteria,":[20],"compress":[21],"both":[22],"the":[23,28,31,43,47,51,59,71,76,88,91,136,140,162,165,168,171,179,184],"vertices":[24,48],"and":[25,98,139,167,181],"edges":[26],"of":[27,38,62,101,109,164,170,183],"graph":[29],"communities,":[32],"which":[33,69,127],"lead":[34],"to":[35,57,82,87,96,129,177],"loss":[37],"edge":[40,72],"information.":[41],"On":[42],"other":[44],"hand,":[45],"compressing":[46],"while":[49],"preserving":[50],"directed-edge":[52],"information":[53,73],"provides":[54],"way":[56],"learn":[58,83],"representation":[61],"graph.":[65],"The":[66],"reconstruction":[67,122],"error,":[68],"measures":[70],"preserved":[74],"by":[75],"summarized":[77,92],"graph,":[78],"can":[79],"be":[80],"used":[81],"such":[84],"representation.":[85],"Compared":[86],"original":[89],"graphs,":[90],"are":[94,99,175],"easier":[95],"analyze":[97],"capable":[100],"extracting":[102],"group-level":[103],"features,":[104],"for":[106],"efficient":[107],"interventions":[108],"population":[110],"behavior.":[111],"In":[112],"this":[113],"letter,":[114],"we":[115],"present":[116],"model,":[118],"minimizing":[121],"error":[123],"with":[124,151],"nonnegative":[125],"constraints,":[126],"relates":[128],"Max-Cut":[131],"criterion":[132],"that":[133],"simultaneously":[134],"identifies":[135],"compressed":[137,142],"nodes":[138],"relations":[143],"between":[144],"these":[145],"nodes.":[146],"A":[147],"multiplicative":[148],"update":[149],"algorithm":[150],"column-wise":[152],"normalization":[153],"proposed.":[155],"We":[156],"further":[157],"provide":[158],"theoretical":[159],"results":[160],"identifiability":[163],"model":[166],"convergence":[169],"proposed":[172,185],"algorithms.":[173],"Experiments":[174],"conducted":[176],"demonstrate":[178],"accuracy":[180],"robustness":[182],"method.":[186]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}