{"id":"https://openalex.org/W3046797186","doi":"https://doi.org/10.1109/tcyb.2020.3033003","title":"Interpretable Rule Discovery Through Bilevel Optimization of Split-Rules of Nonlinear Decision Trees for Classification Problems","display_name":"Interpretable Rule Discovery Through Bilevel Optimization of Split-Rules of Nonlinear Decision Trees for Classification Problems","publication_year":2020,"publication_date":"2020-12-01","ids":{"openalex":"https://openalex.org/W3046797186","doi":"https://doi.org/10.1109/tcyb.2020.3033003","mag":"3046797186","pmid":"https://pubmed.ncbi.nlm.nih.gov/33259315"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2020.3033003","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3033003","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2008.00410","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068379698","display_name":"Yashesh Dhebar","orcid":"https://orcid.org/0000-0001-8144-0566"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yashesh Dhebar","raw_affiliation_strings":["Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA","\u2002Michigan State University"],"raw_orcid":"https://orcid.org/0000-0001-8144-0566","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"\u2002Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088394271","display_name":"Kalyanmoy Deb","orcid":"https://orcid.org/0000-0001-7402-9939"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kalyanmoy Deb","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA","\u2002Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"\u2002Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":0.1343,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58446247,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"51","issue":"11","first_page":"5573","last_page":"5584"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9988999962806702,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9988999962806702,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9968000054359436,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9926999807357788,"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/interpretability","display_name":"Interpretability","score":0.7949963212013245},{"id":"https://openalex.org/keywords/classifier","display_name":"Classifier (UML)","score":0.7010883092880249},{"id":"https://openalex.org/keywords/decision-tree","display_name":"Decision tree","score":0.5868294835090637},{"id":"https://openalex.org/keywords/decision-rule","display_name":"Decision rule","score":0.5020899772644043},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49933528900146484},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4770033657550812},{"id":"https://openalex.org/keywords/binary-classification","display_name":"Binary classification","score":0.4614090025424957},{"id":"https://openalex.org/keywords/linear-classifier","display_name":"Linear classifier","score":0.4296095371246338},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.41309791803359985},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39722415804862976},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3949536681175232},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.345269113779068},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.34513676166534424},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.06854656338691711}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.7949963212013245},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.7010883092880249},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.5868294835090637},{"id":"https://openalex.org/C84839998","wikidata":"https://www.wikidata.org/wiki/Q5249245","display_name":"Decision rule","level":2,"score":0.5020899772644043},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49933528900146484},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4770033657550812},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.4614090025424957},{"id":"https://openalex.org/C139532973","wikidata":"https://www.wikidata.org/wiki/Q2679259","display_name":"Linear classifier","level":3,"score":0.4296095371246338},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.41309791803359985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39722415804862976},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3949536681175232},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.345269113779068},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.34513676166534424},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.06854656338691711}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tcyb.2020.3033003","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3033003","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:33259315","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33259315","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 cybernetics","raw_type":null},{"id":"pmh:oai:arXiv.org:2008.00410","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.00410","pdf_url":"https://arxiv.org/pdf/2008.00410","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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3046797186","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2008.00410","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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2008.00410","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2008.00410","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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2008.00410","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.00410","pdf_url":"https://arxiv.org/pdf/2008.00410","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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7799999713897705}],"awards":[],"funders":[{"id":"https://openalex.org/F4320307109","display_name":"General Motors Corporation","ror":"https://ror.org/05addee68"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3046797186.pdf","grobid_xml":"https://content.openalex.org/works/W3046797186.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W80760317","https://openalex.org/W152751697","https://openalex.org/W225560312","https://openalex.org/W1487855905","https://openalex.org/W1513389696","https://openalex.org/W1515620500","https://openalex.org/W1522059164","https://openalex.org/W1525844566","https://openalex.org/W1527083469","https://openalex.org/W1544969377","https://openalex.org/W1549490638","https://openalex.org/W1550451942","https://openalex.org/W1595498733","https://openalex.org/W1846834309","https://openalex.org/W1873332500","https://openalex.org/W1991347287","https://openalex.org/W2000295051","https://openalex.org/W2003240725","https://openalex.org/W2004575852","https://openalex.org/W2018401509","https://openalex.org/W2050287928","https://openalex.org/W2097932601","https://openalex.org/W2100233488","https://openalex.org/W2102539288","https://openalex.org/W2104046064","https://openalex.org/W2106411961","https://openalex.org/W2109638028","https://openalex.org/W2110905164","https://openalex.org/W2112299196","https://openalex.org/W2113882472","https://openalex.org/W2126105956","https://openalex.org/W2141699448","https://openalex.org/W2148040937","https://openalex.org/W2148143831","https://openalex.org/W2154129931","https://openalex.org/W2156909104","https://openalex.org/W2166716616","https://openalex.org/W2170457874","https://openalex.org/W2398671303","https://openalex.org/W2614367549","https://openalex.org/W2951539267","https://openalex.org/W3008229559","https://openalex.org/W3021613070","https://openalex.org/W3123427206","https://openalex.org/W4244165801","https://openalex.org/W4297957988","https://openalex.org/W6603222281","https://openalex.org/W6608886761","https://openalex.org/W6631173008","https://openalex.org/W6631223166","https://openalex.org/W6632862115","https://openalex.org/W6639175750","https://openalex.org/W6671203228","https://openalex.org/W6676179485","https://openalex.org/W6676885637"],"related_works":["https://openalex.org/W3106710618","https://openalex.org/W3175175767","https://openalex.org/W3153986382","https://openalex.org/W2584281025","https://openalex.org/W2104677983","https://openalex.org/W163275269","https://openalex.org/W2728149462","https://openalex.org/W2294397683","https://openalex.org/W2021790732","https://openalex.org/W3214107269","https://openalex.org/W2322491400","https://openalex.org/W2965335381","https://openalex.org/W3210756005","https://openalex.org/W2886963752","https://openalex.org/W2467980424","https://openalex.org/W1559002010","https://openalex.org/W2133004360","https://openalex.org/W2034232946","https://openalex.org/W3046722445","https://openalex.org/W2547835482"],"abstract_inverted_index":{"For":[0],"supervised":[1],"classification":[2,251],"problems":[3,233],"involving":[4,97],"design,":[5],"control,":[6],"and":[7,138,226,236,249],"other":[8],"practical":[9],"purposes,":[10],"users":[11],"are":[12,234],"not":[13],"only":[14],"interested":[15],"in":[16,59,99,105,167],"finding":[17],"a":[18,39,49,64,69,79,92,155,217],"highly":[19],"accurate":[20],"classifier":[21,29,40,70,148],"but":[22],"they":[23],"also":[24],"demand":[25],"that":[26],"the":[27,34,89,103,106,120,123,129,132,141,144,147,170,181,183,187,196,200,211,243],"obtained":[28,160],"be":[30,57],"easily":[31],"interpretable.":[32],"While":[33],"definition":[35],"of":[36,38,74,88,122,131,140,146,180,192,195,203,210,219,241],"interpretability":[37,145],"can":[41],"vary":[42],"from":[43],"case":[44],"to":[45,56,101,118,198,246],"case,":[46],"here,":[47],"by":[48],"humanly":[50],"interpretable":[51,178],"classifier,":[52],"we":[53,67],"restrict":[54],"it":[55],"expressed":[58],"simplistic":[60],"mathematical":[61,76,94],"terms.":[62],"As":[63],"novel":[65],"approach,":[66],"represent":[68],"as":[71],"an":[72,162,177],"assembly":[73],"simple":[75],"rules":[77],"using":[78,161],"nonlinear":[80,93,152],"decision":[81,142],"tree":[82,90],"(NLDT).":[83],"Each":[84],"conditional":[85,108,136,157],"(nonterminal)":[86],"node":[87,109,137,158],"represents":[91],"rule":[95,197],"(split-rule)":[96],"features":[98],"order":[100],"partition":[102],"dataset":[104],"given":[107,156],"into":[110],"two":[111,204],"nonoverlapping":[112],"subsets.":[113],"This":[114],"partitioning":[115],"is":[116,149,159,214],"intended":[117],"minimize":[119,199],"impurity":[121,202],"resulting":[124,205],"child":[125,206],"nodes.":[126,207],"By":[127],"restricting":[128],"structure":[130,179],"split-rule":[133,153],"at":[134,154,176],"each":[135],"depth":[139],"tree,":[143],"ensured.":[150],"The":[151,208],"evolutionary":[163],"bilevel":[164],"optimization":[165],"algorithm,":[166],"which":[168],"while":[169],"upper":[171],"level":[172,185],"focuses":[173],"on":[174,216,230],"arriving":[175],"split-rule,":[182],"lower":[184],"achieves":[186],"most":[188],"appropriate":[189],"weights":[190],"(coefficients)":[191],"individual":[193],"constituents":[194],"net":[201],"performance":[209],"proposed":[212,244],"algorithm":[213],"demonstrated":[215],"number":[218],"controlled":[220],"test":[221],"problems,":[222,225],"existing":[223],"benchmark":[224],"industrial":[227],"problems.":[228],"Results":[229],"2-500":[231],"feature":[232],"encouraging":[235],"open":[237],"up":[238],"further":[239],"scopes":[240],"applying":[242],"approach":[245],"more":[247],"challenging":[248],"complex":[250],"tasks.":[252]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
