{"id":"https://openalex.org/W2088040029","doi":"https://doi.org/10.1109/cec.2010.5586498","title":"On population diversity measures in Euclidean space","display_name":"On population diversity measures in Euclidean space","publication_year":2010,"publication_date":"2010-07-01","ids":{"openalex":"https://openalex.org/W2088040029","doi":"https://doi.org/10.1109/cec.2010.5586498","mag":"2088040029"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2010.5586498","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2010.5586498","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"},"type":"conference-paper","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/A5047120390","display_name":"Bakir La\u010devi\u0107","orcid":"https://orcid.org/0000-0002-9781-9500"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Bakir Lacevic","raw_affiliation_strings":["Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano, Italy","Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 20133 - Milano, Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 20133 - Milano, Italy#TAB#","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046316138","display_name":"E. Amaldi","orcid":"https://orcid.org/0000-0002-3553-2571"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Edoardo Amaldi","raw_affiliation_strings":["Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano, Italy","Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 20133 - Milano, Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 20133 - Milano, Italy#TAB#","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":4.3826,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.9304175,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9962000250816345,"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"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9962000250816345,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9939000010490417,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6645258665084839},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5814267992973328},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5627170205116272},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5435261130332947},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5299659371376038},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5279844403266907},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5140255689620972},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.4782213866710663},{"id":"https://openalex.org/keywords/euclidean-minimum-spanning-tree","display_name":"Euclidean minimum spanning tree","score":0.4629756808280945},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.4580305218696594},{"id":"https://openalex.org/keywords/distance-measures","display_name":"Distance measures","score":0.45642679929733276},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4515085816383362},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4443613290786743},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4422546625137329},{"id":"https://openalex.org/keywords/euclidean-distance-matrix","display_name":"Euclidean distance matrix","score":0.4387704133987427},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4233439564704895},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.42091965675354004},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35708221793174744},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29446157813072205},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2741393446922302},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2680824398994446},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1616286337375641},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.15973129868507385},{"id":"https://openalex.org/keywords/kruskals-algorithm","display_name":"Kruskal's algorithm","score":0.1447533369064331}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6645258665084839},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5814267992973328},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5627170205116272},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5435261130332947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5299659371376038},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5279844403266907},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5140255689620972},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.4782213866710663},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.4629756808280945},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.4580305218696594},{"id":"https://openalex.org/C2639959","wikidata":"https://www.wikidata.org/wiki/Q1344778","display_name":"Distance measures","level":2,"score":0.45642679929733276},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4515085816383362},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4443613290786743},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4422546625137329},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.4387704133987427},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4233439564704895},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.42091965675354004},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35708221793174744},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29446157813072205},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2741393446922302},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2680824398994446},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1616286337375641},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.15973129868507385},{"id":"https://openalex.org/C63645285","wikidata":"https://www.wikidata.org/wiki/Q797860","display_name":"Kruskal's algorithm","level":3,"score":0.1447533369064331},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cec.2010.5586498","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2010.5586498","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:re.public.polimi.it:11311/573587","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/573587","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W39843496","https://openalex.org/W160321423","https://openalex.org/W1504943474","https://openalex.org/W1586050406","https://openalex.org/W1589038126","https://openalex.org/W1592935101","https://openalex.org/W1605224640","https://openalex.org/W1608919060","https://openalex.org/W1836400055","https://openalex.org/W1966658892","https://openalex.org/W1981745143","https://openalex.org/W2003485756","https://openalex.org/W2003784703","https://openalex.org/W2010847810","https://openalex.org/W2031671531","https://openalex.org/W2032841680","https://openalex.org/W2033108330","https://openalex.org/W2040396531","https://openalex.org/W2042918131","https://openalex.org/W2071112958","https://openalex.org/W2074308169","https://openalex.org/W2083234991","https://openalex.org/W2088592169","https://openalex.org/W2089158547","https://openalex.org/W2112912151","https://openalex.org/W2115629999","https://openalex.org/W2122892819","https://openalex.org/W2123485079","https://openalex.org/W2127166751","https://openalex.org/W2136853134","https://openalex.org/W2149111164","https://openalex.org/W2151953637","https://openalex.org/W2153654820","https://openalex.org/W2162613513","https://openalex.org/W2166963499","https://openalex.org/W2327699610","https://openalex.org/W2463564488","https://openalex.org/W2915069135","https://openalex.org/W4237390087","https://openalex.org/W4285719527","https://openalex.org/W6601658840","https://openalex.org/W6606689408","https://openalex.org/W6635048620","https://openalex.org/W6635289253","https://openalex.org/W6658731229","https://openalex.org/W6678551067"],"related_works":["https://openalex.org/W1561849181","https://openalex.org/W3187208706","https://openalex.org/W3081212354","https://openalex.org/W98489388","https://openalex.org/W3116169590","https://openalex.org/W1985149601","https://openalex.org/W3101281637","https://openalex.org/W1703428550","https://openalex.org/W1964611452","https://openalex.org/W2390742649"],"abstract_inverted_index":{"In":[0,43],"this":[1],"paper":[2],"we":[3,27,38,45],"define":[4],"a":[5,47,55,79],"mathematical":[6],"notion":[7],"of":[8,16,33,57,82,95,117],"ectropy":[9],"for":[10],"classifying":[11],"diversity":[12],"measures":[13,36,61,64,73],"in":[14,115],"terms":[15,116],"the":[17,29,93,97,111,118,121,125],"extent":[18],"to":[19,23,92,109],"which":[20],"they":[21],"tend":[22],"penalize":[24],"point":[25],"collocation,":[26],"investigate":[28],"advantages":[30],"and":[31,37,62,76,84,124],"disadvantages":[32],"several":[34],"known":[35],"propose":[39],"some":[40],"novel":[41],"ones.":[42],"particular,":[44],"introduce":[46],"measure":[48,100],"based":[49,60,65,101],"on":[50,66,78,102],"Euclidean":[51,103],"minimum":[52,104],"spanning":[53,105],"trees,":[54],"class":[56],"power":[58],"mean":[59],"three":[63],"discrepancy":[67],"from":[68],"uniform":[69],"distribution.":[70],"All":[71],"considered":[72],"are":[74],"tested":[75],"compared":[77],"large":[80],"set":[81],"random":[83],"structured":[85],"populations.":[86],"Special":[87],"attention":[88],"is":[89],"also":[90],"devoted":[91],"complexity":[94,123],"computing":[96],"measures.":[98],"The":[99],"trees":[106],"turns":[107],"out":[108],"be":[110],"most":[112],"promising":[113],"one":[114],"tradeoff":[119],"between":[120],"computational":[122],"ectropic":[126],"behavior.":[127]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}