{"id":"https://openalex.org/W2771012806","doi":"https://doi.org/10.1007/s10100-017-0499-2","title":"Building a completely positive factorization","display_name":"Building a completely positive factorization","publication_year":2017,"publication_date":"2017-11-15","ids":{"openalex":"https://openalex.org/W2771012806","doi":"https://doi.org/10.1007/s10100-017-0499-2","mag":"2771012806","pmid":"https://pubmed.ncbi.nlm.nih.gov/29773964"},"language":"en","primary_location":{"id":"doi:10.1007/s10100-017-0499-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10100-017-0499-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10100-017-0499-2.pdf","source":{"id":"https://openalex.org/S161053114","display_name":"Central European Journal of Operations Research","issn_l":"1435-246X","issn":["1435-246X","1613-9178"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Central European Journal of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10100-017-0499-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023776719","display_name":"Immanuel M. Bomze","orcid":"https://orcid.org/0000-0002-6288-9226"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Immanuel M. Bomze","raw_affiliation_strings":["ISOR and VCOR, University of Vienna, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"ISOR and VCOR, University of Vienna, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023776719"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.5841,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.71162482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"2","first_page":"287","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9979000091552734,"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/T12504","display_name":"Mathematics and Applications","score":0.9519000053405762,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7654906511306763},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6892715096473694},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6126025915145874},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6088120937347412},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6063698530197144},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5593478679656982},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5313758254051208},{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.49917125701904297},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16462409496307373},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.15443763136863708},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13821646571159363},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07420864701271057}],"concepts":[{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7654906511306763},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6892715096473694},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6126025915145874},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6088120937347412},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6063698530197144},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5593478679656982},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5313758254051208},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.49917125701904297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16462409496307373},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.15443763136863708},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13821646571159363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07420864701271057},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10100-017-0499-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10100-017-0499-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10100-017-0499-2.pdf","source":{"id":"https://openalex.org/S161053114","display_name":"Central European Journal of Operations Research","issn_l":"1435-246X","issn":["1435-246X","1613-9178"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Central European Journal of Operations Research","raw_type":"journal-article"},{"id":"pmid:29773964","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29773964","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":"Central European journal of operations research","raw_type":null},{"id":"pmh:info:fedora/oai:univie.ac.at:o:691461","is_oa":true,"landing_page_url":"https://phaidra.univie.ac.at/o:691461","pdf_url":null,"source":{"id":"https://openalex.org/S4306401993","display_name":"Phaidra (Universit\u00e4t Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129774422","host_organization_name":"University of Vienna","host_organization_lineage":["https://openalex.org/I129774422"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1435-246X","raw_type":"article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.473.118","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.473.118","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2009/08/2381.pdf","raw_type":"text"},{"id":"pmh:oai:RePEc:spr:cejnor:v:26:y:2018:i:2:d:10.1007_s10100-017-0499-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10100-017-0499-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:europepmc.org:4871212","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5945802","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s10100-017-0499-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10100-017-0499-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10100-017-0499-2.pdf","source":{"id":"https://openalex.org/S161053114","display_name":"Central European Journal of Operations Research","issn_l":"1435-246X","issn":["1435-246X","1613-9178"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Central European Journal of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321691","display_name":"Universit\u00e4t Wien","ror":"https://ror.org/03prydq77"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2771012806.pdf","grobid_xml":"https://content.openalex.org/works/W2771012806.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W107432625","https://openalex.org/W167979754","https://openalex.org/W229771843","https://openalex.org/W598314002","https://openalex.org/W1549791526","https://openalex.org/W1562905296","https://openalex.org/W1729990846","https://openalex.org/W1966805253","https://openalex.org/W1969120667","https://openalex.org/W1969807530","https://openalex.org/W1970270635","https://openalex.org/W1991320936","https://openalex.org/W2001392214","https://openalex.org/W2012956404","https://openalex.org/W2015775145","https://openalex.org/W2018776261","https://openalex.org/W2023336262","https://openalex.org/W2025776604","https://openalex.org/W2025986033","https://openalex.org/W2026654387","https://openalex.org/W2028158177","https://openalex.org/W2034632843","https://openalex.org/W2038163734","https://openalex.org/W2040500267","https://openalex.org/W2043470680","https://openalex.org/W2044177072","https://openalex.org/W2045426493","https://openalex.org/W2061781854","https://openalex.org/W2070524150","https://openalex.org/W2078600458","https://openalex.org/W2081494214","https://openalex.org/W2083346319","https://openalex.org/W2094304614","https://openalex.org/W2095393540","https://openalex.org/W2095471868","https://openalex.org/W2099779699","https://openalex.org/W2103765204","https://openalex.org/W2107285505","https://openalex.org/W2107888388","https://openalex.org/W2111617833","https://openalex.org/W2124345338","https://openalex.org/W2124487034","https://openalex.org/W2140320282","https://openalex.org/W2144359569","https://openalex.org/W2160625469","https://openalex.org/W2162985064","https://openalex.org/W2315226988","https://openalex.org/W2344697147","https://openalex.org/W2366960062","https://openalex.org/W2553508462","https://openalex.org/W2762341112","https://openalex.org/W2962797255","https://openalex.org/W3036596190","https://openalex.org/W3106299813","https://openalex.org/W4232173585","https://openalex.org/W4248179398","https://openalex.org/W4302087481"],"related_works":["https://openalex.org/W772650738","https://openalex.org/W2013985456","https://openalex.org/W2951564084","https://openalex.org/W4302984940","https://openalex.org/W2776807270","https://openalex.org/W3030085148","https://openalex.org/W2392685819","https://openalex.org/W2140318696","https://openalex.org/W1973739845","https://openalex.org/W119752240"],"abstract_inverted_index":{"A":[0],"symmetric":[1,14],"matrix":[2,21,42,91],"of":[3,18,43,50,54,87,106],"order":[4],"<i>n</i>":[5,23,44],"is":[6,131],"called":[7],"<i>completely":[8],"positive</i>":[9],"if":[10,34],"it":[11,35],"has":[12],"a":[13,19,40,95,107],"factorization":[15,105,121],"by":[16],"means":[17],"rectangular":[20],"with":[22],"columns":[24],"and":[25,66,82,98],"no":[26],"negative":[27],"entries":[28],"(a":[29],"so-called":[30],"<i>cp":[31],"factorization</i>),":[32],"i.e.,":[33],"can":[36,117],"be":[37,80],"interpreted":[38],"as":[39],"Gram":[41],"directions":[45,78],"in":[46,134],"the":[47,73,77,88,123,129],"positive":[48],"orthant":[49],"another":[51],"Euclidean":[52],"space":[53],"possibly":[55],"different":[56],"dimension.":[57,71],"Finding":[58],"this":[59,119],"factor":[60],"therefore":[61],"amounts":[62],"to":[63,122],"angle":[64],"packing":[65],"finding":[67],"an":[68,101],"appropriate":[69],"embedding":[70,74],"Neither":[72],"dimension":[75],"nor":[76],"may":[79,92],"unique,":[81],"so":[83],"many":[84],"cp":[85,104,120],"factorizations":[86],"same":[89],"given":[90],"coexist.":[93],"Using":[94],"bordering":[96],"approach,":[97],"building":[99],"upon":[100],"already":[102],"known":[103],"principal":[108],"block,":[109],"we":[110,116],"establish":[111],"sufficient":[112],"conditions":[113],"under":[114],"which":[115],"extend":[118],"full":[124],"matrix.":[125],"Simulations":[126],"show":[127],"that":[128],"approach":[130],"promising":[132],"also":[133],"higher":[135],"dimensions.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
