{"id":"https://openalex.org/W2038718434","doi":"https://doi.org/10.1002/1098-111x(200010)15:10<959::aid-int4>3.0.co;2-b","title":"Why clustering in function approximation? Theoretical explanation","display_name":"Why clustering in function approximation? Theoretical explanation","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2038718434","doi":"https://doi.org/10.1002/1098-111x(200010)15:10<959::aid-int4>3.0.co;2-b","mag":"2038718434"},"language":"en","primary_location":{"id":"doi:10.1002/1098-111x(200010)15:10<959::aid-int4>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1098-111x(200010)15:10<959::aid-int4>3.0.co;2-b","pdf_url":null,"source":{"id":"https://openalex.org/S57950554","display_name":"International Journal of Intelligent Systems","issn_l":"0884-8173","issn":["0884-8173","1098-111X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Intelligent Systems","raw_type":"journal-article"},"type":"article","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/A5061275811","display_name":"\u0412\u043b\u0430\u0434\u0438\u043a \u041a\u0440\u0435\u0439\u043d\u043e\u0432\u0438\u0447","orcid":"https://orcid.org/0000-0002-1244-1650"},"institutions":[{"id":"https://openalex.org/I164936912","display_name":"The University of Texas at El Paso","ror":"https://ror.org/04d5vba33","country_code":"US","type":"education","lineage":["https://openalex.org/I164936912"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Vladik Kreinovich","raw_affiliation_strings":["Department of Computer Science, University of Texas at El Paso, El Paso, Texas 79968, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Texas at El Paso, El Paso, Texas 79968, USA","institution_ids":["https://openalex.org/I164936912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057214563","display_name":"Yeung Yam","orcid":"https://orcid.org/0000-0001-9950-5794"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yeung Yam","raw_affiliation_strings":["Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061275811"],"corresponding_institution_ids":["https://openalex.org/I164936912"],"apc_list":{"value":2500,"currency":"USD","value_usd":2500},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.1591463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"10","first_page":"959","last_page":"966"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9577999711036682,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/cluster-analysis","display_name":"Cluster analysis","score":0.6631844639778137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6190154552459717},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5501594543457031},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.5332075953483582},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.5246251225471497},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.44825810194015503},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41233232617378235},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35288316011428833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.260034441947937},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.1721976399421692},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15233764052391052},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13375219702720642}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6631844639778137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6190154552459717},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5501594543457031},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.5332075953483582},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.5246251225471497},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.44825810194015503},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41233232617378235},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35288316011428833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.260034441947937},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.1721976399421692},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15233764052391052},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13375219702720642},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1002/1098-111x(200010)15:10<959::aid-int4>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1098-111x(200010)15:10<959::aid-int4>3.0.co;2-b","pdf_url":null,"source":{"id":"https://openalex.org/S57950554","display_name":"International Journal of Intelligent Systems","issn_l":"0884-8173","issn":["0884-8173","1098-111X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.utep.edu:cs_techrep-1515","is_oa":false,"landing_page_url":"https://digitalcommons.utep.edu/cs_techrep/515","pdf_url":null,"source":{"id":"https://openalex.org/S4377196403","display_name":"scholarworks - UTEP (The University of Texas at El Paso)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I164936912","host_organization_name":"The University of Texas at El Paso","host_organization_lineage":["https://openalex.org/I164936912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Departmental Technical Reports (CS)","raw_type":"text"},{"id":"pmh:oai:scholarworks.utep.edu:cs_techrep-1515","is_oa":false,"landing_page_url":"https://scholarworks.utep.edu/cs_techrep/515","pdf_url":null,"source":{"id":"https://openalex.org/S4377196403","display_name":"scholarworks - UTEP (The University of Texas at El Paso)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I164936912","host_organization_name":"The University of Texas at El Paso","host_organization_lineage":["https://openalex.org/I164936912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Departmental Technical Reports (CS)","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.48.759","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.759","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cs.utep.edu/vladik/1999/tr99-3.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.75.2422","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.2422","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.utep.edu/vladik/1999/tr99-3.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W646851550","https://openalex.org/W1542813816","https://openalex.org/W1561414385","https://openalex.org/W1570834090","https://openalex.org/W1990368529","https://openalex.org/W1995365180","https://openalex.org/W2007042673","https://openalex.org/W2027006788","https://openalex.org/W2029906715","https://openalex.org/W2046778278","https://openalex.org/W2113076747","https://openalex.org/W2135346934","https://openalex.org/W2139585733","https://openalex.org/W2152867250","https://openalex.org/W2156415214","https://openalex.org/W2316584926","https://openalex.org/W6648829021","https://openalex.org/W6679986405"],"related_works":["https://openalex.org/W1893285581","https://openalex.org/W2095736209","https://openalex.org/W4313271098","https://openalex.org/W3119134791","https://openalex.org/W2801788073","https://openalex.org/W228596958","https://openalex.org/W4387422913","https://openalex.org/W2132201882","https://openalex.org/W3109377487","https://openalex.org/W4360879481"],"abstract_inverted_index":{"Function":[0],"approximation":[1,104,207],"is":[2,29,59,208],"a":[3,34,43,64],"very":[4],"important":[5],"practical":[6,10],"problem:":[7],"in":[8,78],"many":[9,100,127],"applications,":[11],"we":[12,32],"know":[13],"the":[14,18,55,90,131,134,139,178,210],"exact":[15,27],"form":[16],"of":[17,36,45,89,95,110,130,137,189,213],"functional":[19],"dependence":[20,28],"y=f(x1,\u2026,xn)":[21],"between":[22],"physical":[23],"quantities,":[24],"but":[25],"this":[26,70,115,156],"complicated,":[30],"so":[31,121],"need":[33],"lot":[35,44],"computer":[37],"space":[38],"to":[39,47,51,62,103,154,184,203],"store":[40],"it,":[41,49],"and":[42,84,162],"time":[46],"process":[48],"i.e.,":[50,187],"predict":[52],"y":[53],"from":[54],"given":[56],"xi.":[57],"It":[58],"therefore":[60],"necessary":[61],"find":[63],"simpler":[65],"approximate":[66],"expression":[67],"g(x1,\u2026,xn)\u2248f(x1,\u2026,xn)":[68],"for":[69,81,120,126,168],"same":[71],"dependence.":[72],"This":[73],"problem":[74,116,157],"has":[75,117],"been":[76,118,144,152],"analyzed":[77,93,119],"numerical":[79],"mathematics":[80],"several":[82],"centuries,":[83],"it":[85],"is,":[86],"therefore,":[87],"one":[88],"most":[91,169],"thoroughly":[92],"problems":[94,136],"applied":[96,153],"mathematics.":[97],"There":[98],"are":[99,175],"results":[101],"related":[102],"by":[105],"polynomials,":[106,108],"trigonometric":[107],"splines":[109],"different":[111],"type,":[112],"etc.":[113],"Since":[114],"long,":[122],"no":[123],"wonder":[124],"that":[125,195],"reasonable":[128,199],"formulations":[129],"optimality":[132,171],"criteria,":[133,172],"corresponding":[135],"finding":[138],"optimal":[140,173,211],"approximations":[141,174,188],"have":[142,151],"already":[143,176],"solved.":[145],"Lately,":[146],"however,":[147,194],"new":[148,198],"clustering-related":[149],"techniques":[150],"solve":[155],"(by":[158],"Yager,":[159],"Filev,":[160],"Chu,":[161],"others).":[163],"At":[164],"first":[165],"glance,":[166],"since":[167],"traditional":[170],"known,":[177],"clustering":[179],"approach":[180],"can":[181],"only":[182],"lead":[183],"non-optimal":[185],"approximations,":[186],"inferior":[190],"quality.":[191],"We":[192],"show,":[193],"there":[196],"exist":[197],"criteria":[200],"with":[201],"respect":[202],"which":[204],"clustering-based":[205],"function":[206,214],"indeed":[209],"method":[212],"approximation.":[215],"\u00a9":[216],"2000":[217],"John":[218],"Wiley":[219],"&":[220],"Sons,":[221],"Inc.":[222]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}