{"id":"https://openalex.org/W96410031","doi":"https://doi.org/10.1007/978-3-319-00035-0_16","title":"Convex Optimization as a Tool for Correcting Dissimilarity Matrices for Regular Minimality","display_name":"Convex Optimization as a Tool for Correcting Dissimilarity Matrices for Regular Minimality","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W96410031","doi":"https://doi.org/10.1007/978-3-319-00035-0_16","mag":"96410031"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-00035-0_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-00035-0_16","pdf_url":null,"source":{"id":"https://openalex.org/S4210194094","display_name":"Studies in classification, data analysis, and knowledge organization","issn_l":"1431-8814","issn":["1431-8814","2198-3321"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studies in Classification, Data Analysis, and Knowledge Organization","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/A5057828595","display_name":"Matthias Trendtel","orcid":"https://orcid.org/0000-0003-3724-6736"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Matthias Trendtel","raw_affiliation_strings":["Division for Methodology and Statistics, Federal Institute for Educational Research, Innovation & Development of the Austrian School System (BIFIE), Salzburg, Austria"],"affiliations":[{"raw_affiliation_string":"Division for Methodology and Statistics, Federal Institute for Educational Research, Innovation & Development of the Austrian School System (BIFIE), Salzburg, Austria","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025566009","display_name":"Ali \u00dcnl\u00fc","orcid":"https://orcid.org/0000-0002-6941-5074"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ali \u00dcnl\u00fc","raw_affiliation_strings":["Chair for Methods in Empirical Educational Research, TUM School of Education, Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany"],"affiliations":[{"raw_affiliation_string":"Chair for Methods in Empirical Educational Research, TUM School of Education, Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057828595"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0492826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"165","last_page":"174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.965399980545044,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12417","display_name":"Morphological variations and asymmetry","score":0.965399980545044,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10427","display_name":"Visual perception and processing mechanisms","score":0.9412000179290771,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9394999742507935,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6452965140342712},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6262878179550171},{"id":"https://openalex.org/keywords/multidimensional-scaling","display_name":"Multidimensional scaling","score":0.5977686047554016},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.592103123664856},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5801090598106384},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5531182289123535},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5511780977249146},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5264483094215393},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5074071288108826},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5044058561325073},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4936126470565796},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.48580169677734375},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45771732926368713},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4546213746070862},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.41841909289360046},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37145453691482544},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35884422063827515},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3352792263031006},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26103681325912476},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06647861003875732},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06265532970428467},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05741491913795471}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6452965140342712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6262878179550171},{"id":"https://openalex.org/C91682802","wikidata":"https://www.wikidata.org/wiki/Q620538","display_name":"Multidimensional scaling","level":2,"score":0.5977686047554016},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.592103123664856},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5801090598106384},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5531182289123535},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5511780977249146},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5264483094215393},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5074071288108826},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5044058561325073},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4936126470565796},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.48580169677734375},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45771732926368713},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4546213746070862},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.41841909289360046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37145453691482544},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35884422063827515},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3352792263031006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26103681325912476},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06647861003875732},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06265532970428467},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05741491913795471},{"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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-00035-0_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-00035-0_16","pdf_url":null,"source":{"id":"https://openalex.org/S4210194094","display_name":"Studies in classification, data analysis, and knowledge organization","issn_l":"1431-8814","issn":["1431-8814","2198-3321"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studies in Classification, Data Analysis, and Knowledge Organization","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"},{"score":0.4699999988079071,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W360528349","https://openalex.org/W1503425191","https://openalex.org/W1653619892","https://openalex.org/W1991171156","https://openalex.org/W2034039267","https://openalex.org/W2068845866","https://openalex.org/W2087213364","https://openalex.org/W2159307101","https://openalex.org/W2160858394","https://openalex.org/W2200328892","https://openalex.org/W2296319761","https://openalex.org/W2468285490","https://openalex.org/W2594786969","https://openalex.org/W2955198501","https://openalex.org/W4246354968","https://openalex.org/W4301021743","https://openalex.org/W6665018949","https://openalex.org/W6683860772","https://openalex.org/W6776878035"],"related_works":["https://openalex.org/W4200285273","https://openalex.org/W2374778813","https://openalex.org/W1582127415","https://openalex.org/W2012281976","https://openalex.org/W4238212629","https://openalex.org/W2366040363","https://openalex.org/W2123792622","https://openalex.org/W1001008648","https://openalex.org/W2331122176","https://openalex.org/W2105228010"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}