{"id":"https://openalex.org/W1530623429","doi":"https://doi.org/10.1007/3-540-59119-2_180","title":"Approximation and learning of convex superpositions","display_name":"Approximation and learning of convex superpositions","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1530623429","doi":"https://doi.org/10.1007/3-540-59119-2_180","mag":"1530623429"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-59119-2_180","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-59119-2_180","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"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/A5022317936","display_name":"Leonid Gurvits","orcid":"https://orcid.org/0000-0002-0694-2459"},"institutions":[{"id":"https://openalex.org/I1325886976","display_name":"Siemens (Germany)","ror":"https://ror.org/059mq0909","country_code":"DE","type":"company","lineage":["https://openalex.org/I1325886976"]},{"id":"https://openalex.org/I4210137693","display_name":"Siemens (United States)","ror":"https://ror.org/04axb7e79","country_code":"US","type":"company","lineage":["https://openalex.org/I1325886976","https://openalex.org/I4210137693"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Leonid Gurvits","raw_affiliation_strings":["Siemens Corporate Research, 08540, Princeton, NJ","SIEMENS CORPORATE RESEARCH"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Siemens Corporate Research, 08540, Princeton, NJ","institution_ids":["https://openalex.org/I4210137693"]},{"raw_affiliation_string":"SIEMENS CORPORATE RESEARCH","institution_ids":["https://openalex.org/I1325886976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105512963","display_name":"Pascal Koiran","orcid":"https://orcid.org/0000-0003-3405-7155"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I2799411422","display_name":"Center for Discrete Mathematics and Theoretical Computer Science","ror":"https://ror.org/00k551w06","country_code":"US","type":"facility","lineage":["https://openalex.org/I102322142","https://openalex.org/I118347220","https://openalex.org/I1283103587","https://openalex.org/I1311060795","https://openalex.org/I20089843","https://openalex.org/I2799411422","https://openalex.org/I4210107353"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pascal Koiran","raw_affiliation_strings":["DIMACS, Rutgers University, 08901, New Brunswick, NJ","Rutgers, University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DIMACS, Rutgers University, 08901, New Brunswick, NJ","institution_ids":["https://openalex.org/I2799411422","https://openalex.org/I102322142"]},{"raw_affiliation_string":"Rutgers, University","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":6.0506,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.9685802,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"222","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998000264167786,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9998000264167786,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9726999998092651,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9675999879837036,"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/dimension","display_name":"Dimension (graph theory)","score":0.7854797840118408},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.7543295621871948},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.7372140884399414},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7229621410369873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6676557064056396},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6002032160758972},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6000944972038269},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5736287236213684},{"id":"https://openalex.org/keywords/vc-dimension","display_name":"VC dimension","score":0.5445970296859741},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.47678378224372864},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4603419601917267},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4179947078227997},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.361230731010437},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35621175169944763},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22187942266464233},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.196669340133667},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1336597204208374},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05972251296043396}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7854797840118408},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7543295621871948},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.7372140884399414},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7229621410369873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6676557064056396},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6002032160758972},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6000944972038269},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5736287236213684},{"id":"https://openalex.org/C119322782","wikidata":"https://www.wikidata.org/wiki/Q2662236","display_name":"VC dimension","level":2,"score":0.5445970296859741},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.47678378224372864},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4603419601917267},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4179947078227997},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.361230731010437},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35621175169944763},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22187942266464233},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.196669340133667},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1336597204208374},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05972251296043396},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-59119-2_180","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-59119-2_180","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.550000011920929,"display_name":"Climate action"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W5594912","https://openalex.org/W188867022","https://openalex.org/W1530699444","https://openalex.org/W1561681248","https://openalex.org/W2010029425","https://openalex.org/W2041613709","https://openalex.org/W2059811159","https://openalex.org/W2061905469","https://openalex.org/W2068589781","https://openalex.org/W2084544490","https://openalex.org/W2125053431","https://openalex.org/W2129192653","https://openalex.org/W2154952480","https://openalex.org/W2165758113","https://openalex.org/W2166116275","https://openalex.org/W4248693963","https://openalex.org/W4292025355","https://openalex.org/W4301425558"],"related_works":["https://openalex.org/W2467926385","https://openalex.org/W161301265","https://openalex.org/W2483619716","https://openalex.org/W2377576908","https://openalex.org/W4246461909","https://openalex.org/W563487689","https://openalex.org/W2893068807","https://openalex.org/W2971424936","https://openalex.org/W2007256320","https://openalex.org/W2965861863"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}