{"id":"https://openalex.org/W3136353561","doi":"https://doi.org/10.1093/bioinformatics/btab182","title":"Multiscale part mutual information for quantifying nonlinear direct associations in networks","display_name":"Multiscale part mutual information for quantifying nonlinear direct associations in networks","publication_year":2021,"publication_date":"2021-03-15","ids":{"openalex":"https://openalex.org/W3136353561","doi":"https://doi.org/10.1093/bioinformatics/btab182","mag":"3136353561","pmid":"https://pubmed.ncbi.nlm.nih.gov/33730153"},"language":"en","primary_location":{"id":"doi:10.1093/bioinformatics/btab182","is_oa":false,"landing_page_url":"https://doi.org/10.1093/bioinformatics/btab182","pdf_url":null,"source":{"id":"https://openalex.org/S52395412","display_name":"Bioinformatics","issn_l":"1367-4803","issn":["1367-4803","1367-4811"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bioinformatics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","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/A5007539735","display_name":"Junliang Shang","orcid":"https://orcid.org/0000-0002-8488-2228"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junliang Shang","raw_affiliation_strings":["School of Computer Science, Qufu Normal University , Rizhao 276826, China"],"raw_orcid":"https://orcid.org/0000-0002-8488-2228","affiliations":[{"raw_affiliation_string":"School of Computer Science, Qufu Normal University , Rizhao 276826, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101984165","display_name":"Jing Wang","orcid":"https://orcid.org/0000-0002-9653-7253"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Wang","raw_affiliation_strings":["School of Computer Science, Qufu Normal University , Rizhao 276826, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Qufu Normal University , Rizhao 276826, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055416795","display_name":"Yan Sun","orcid":"https://orcid.org/0000-0002-5080-0781"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Sun","raw_affiliation_strings":["School of Computer Science, Qufu Normal University , Rizhao 276826, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Qufu Normal University , Rizhao 276826, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100448913","display_name":"Feng Li","orcid":"https://orcid.org/0000-0002-5556-3789"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Li","raw_affiliation_strings":["School of Computer Science, Qufu Normal University , Rizhao 276826, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Qufu Normal University , Rizhao 276826, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073144090","display_name":"Jin\u2010Xing Liu","orcid":"https://orcid.org/0000-0001-6104-2149"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin-Xing Liu","raw_affiliation_strings":["School of Computer Science, Qufu Normal University , Rizhao 276826, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Qufu Normal University , Rizhao 276826, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100724184","display_name":"Honghai Zhang","orcid":"https://orcid.org/0000-0002-5010-2502"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Honghai Zhang","raw_affiliation_strings":["College of Life Science, Qufu Normal University , Qufu 273165, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Life Science, Qufu Normal University , Qufu 273165, China","institution_ids":["https://openalex.org/I202126657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100724184"],"corresponding_institution_ids":["https://openalex.org/I202126657"],"apc_list":{"value":3618,"currency":"USD","value_usd":3618},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01856583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"37","issue":"18","first_page":"2920","last_page":"2929"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.20100000500679016,"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"}},"topics":[{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.20100000500679016,"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"}},{"id":"https://openalex.org/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.09669999778270721,"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"}},{"id":"https://openalex.org/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.0746999979019165,"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/mutual-information","display_name":"Mutual information","score":0.7616785764694214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6059634685516357},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5631639957427979},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3905593752861023},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.35050302743911743},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34332776069641113},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.31667977571487427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21344038844108582},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07998055219650269}],"concepts":[{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.7616785764694214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6059634685516357},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5631639957427979},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3905593752861023},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.35050302743911743},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34332776069641113},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31667977571487427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21344038844108582},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07998055219650269},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D005909","descriptor_name":"Glioblastoma","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005909","descriptor_name":"Glioblastoma","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005909","descriptor_name":"Glioblastoma","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012984","descriptor_name":"Software","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012984","descriptor_name":"Software","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012984","descriptor_name":"Software","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1093/bioinformatics/btab182","is_oa":false,"landing_page_url":"https://doi.org/10.1093/bioinformatics/btab182","pdf_url":null,"source":{"id":"https://openalex.org/S52395412","display_name":"Bioinformatics","issn_l":"1367-4803","issn":["1367-4803","1367-4811"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bioinformatics","raw_type":"journal-article"},{"id":"pmid:33730153","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33730153","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":"Bioinformatics (Oxford, England)","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"awards":[{"id":"https://openalex.org/G5609717784","display_name":"\u57fa\u4e8e\u4f4e\u79e9\u548c\u56fe\u6b63\u5219\u7ea6\u675f\u7684\u77e9\u9635\u5206\u89e3\u65b9\u6cd5\u7814\u7a76\u53ca\u5728\u764c\u75c7\u591a\u7ec4\u5b66\u6570\u636e\u4e2d\u7684\u5e94\u7528","funder_award_id":"61872220","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6334930974","display_name":"\u590d\u6742\u75be\u75c5\u5168\u57fa\u56e0\u7ec4SNP\u9ad8\u9636\u4e92\u4f5c\u6a21\u5f0f\u7684\u7f51\u7edc\u6316\u6398\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61972226","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7974007073","display_name":null,"funder_award_id":"61902216","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G800912246","display_name":null,"funder_award_id":"31872242","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8204186601","display_name":null,"funder_award_id":"2018M642635","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1635484243","https://openalex.org/W1981796233","https://openalex.org/W2007347740","https://openalex.org/W2023036714","https://openalex.org/W2027557822","https://openalex.org/W2027607571","https://openalex.org/W2056013836","https://openalex.org/W2070678529","https://openalex.org/W2071330660","https://openalex.org/W2082290707","https://openalex.org/W2090606877","https://openalex.org/W2094680524","https://openalex.org/W2099380913","https://openalex.org/W2102471334","https://openalex.org/W2107879036","https://openalex.org/W2111384508","https://openalex.org/W2122708083","https://openalex.org/W2129794000","https://openalex.org/W2139020869","https://openalex.org/W2146152876","https://openalex.org/W2149350210","https://openalex.org/W2152482800","https://openalex.org/W2161409973","https://openalex.org/W2165700458","https://openalex.org/W2326655560","https://openalex.org/W2337819340","https://openalex.org/W2343938190","https://openalex.org/W2626431107","https://openalex.org/W2737095280","https://openalex.org/W2747889391","https://openalex.org/W2779432642","https://openalex.org/W2789192249","https://openalex.org/W2808711325","https://openalex.org/W2810146973","https://openalex.org/W2813447943","https://openalex.org/W2892171265","https://openalex.org/W2920676536","https://openalex.org/W2964121406","https://openalex.org/W2965757567","https://openalex.org/W2969458782","https://openalex.org/W2974199621","https://openalex.org/W3030256244","https://openalex.org/W3098590676","https://openalex.org/W4247458062","https://openalex.org/W6675273826"],"related_works":["https://openalex.org/W2466816617","https://openalex.org/W1970834875","https://openalex.org/W3174028392","https://openalex.org/W842936808","https://openalex.org/W2000517284","https://openalex.org/W2136503713","https://openalex.org/W2365318811","https://openalex.org/W2375330620","https://openalex.org/W2913710507","https://openalex.org/W2363755581"],"abstract_inverted_index":{"MOTIVATION:":[0],"For":[1],"network-assisted":[2],"analysis,":[3],"which":[4],"has":[5],"become":[6],"a":[7,16,101],"popular":[8],"method":[9],"of":[10,26,33,116,121,154,191],"data":[11,201],"mining,":[12],"network":[13,103],"construction":[14,20],"is":[15,168,193],"crucial":[17],"task.":[18],"Network":[19],"relies":[21],"on":[22,59,136,140],"the":[23,52,87,122,127,147,166],"accurate":[24],"quantification":[25,40,111],"direct":[27,46,75,176],"associations":[28,35,76,177],"among":[29,36,77],"variables.":[30],"The":[31,188],"existence":[32],"multiscale":[34,53,82,183],"variables":[37,78],"presents":[38],"several":[39],"challenges,":[41],"especially":[42,180],"when":[43],"quantifying":[44,73,174],"nonlinear":[45,65,74,175],"interactions.":[47],"RESULTS:":[48],"In":[49],"this":[50],"study,":[51],"part":[54,60],"mutual":[55,61,132],"information":[56,62,133],"(MPMI),":[57],"based":[58],"(PMI)":[63],"and":[64,91,124,130,139,156],"partial":[66],"association":[67],"(NPA),":[68],"was":[69,104,149],"developed":[70],"for":[71,173],"effectively":[72],"in":[79,89,100,178],"networks":[80],"with":[81,126,182],"associations.":[83,118,184],"First,":[84],"we":[85],"defined":[86],"MPMI":[88,123,148,167,192],"theory":[90],"derived":[92],"its":[93,110,161],"five":[94],"important":[95],"properties.":[96],"Second,":[97],"an":[98,169],"experiment":[99],"three-node":[102],"carried":[105],"out":[106],"to":[107,151,159],"numerically":[108],"estimate":[109],"ability":[112],"under":[113],"two":[114],"cases":[115],"strong":[117],"Third,":[119],"experiments":[120],"comparisons":[125],"PMI,":[128],"NPA":[129],"conditional":[131],"were":[134],"performed":[135],"simulated":[137],"datasets":[138,141,153],"from":[142],"DREAM":[143],"challenge":[144],"project.":[145],"Finally,":[146],"applied":[150],"real":[152],"glioblastoma":[155],"lung":[157],"adenocarcinoma":[158],"validate":[160],"effectiveness.":[162],"Results":[163],"showed":[164],"that":[165],"effective":[170],"alternative":[171],"measure":[172],"networks,":[179],"those":[181],"AVAILABILITY":[185],"AND":[186],"IMPLEMENTATION:":[187],"source":[189],"code":[190],"available":[194,203],"online":[195],"at":[196,204],"https://github.com/CDMB-lab/MPMI.":[197],"SUPPLEMENTARY":[198],"INFORMATION:":[199],"Supplementary":[200],"are":[202],"Bioinformatics":[205],"online.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}