{"id":"https://openalex.org/W2048687561","doi":"https://doi.org/10.1155/2008/764206","title":"Theorems on Positive Data: On the Uniqueness of NMF","display_name":"Theorems on Positive Data: On the Uniqueness of NMF","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2048687561","doi":"https://doi.org/10.1155/2008/764206","mag":"2048687561","pmid":"https://pubmed.ncbi.nlm.nih.gov/18497868"},"language":"en","primary_location":{"id":"doi:10.1155/2008/764206","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/764206","pdf_url":"https://downloads.hindawi.com/journals/cin/2008/764206.pdf","source":{"id":"https://openalex.org/S72372694","display_name":"Computational Intelligence and Neuroscience","issn_l":"1687-5265","issn":["1687-5265","1687-5273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Intelligence and Neuroscience","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/cin/2008/764206.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025879904","display_name":"Hans Laurberg","orcid":null},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Hans Laurberg","raw_affiliation_strings":["Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026658144","display_name":"Mads Gr\u00e6sb\u00f8ll Christensen","orcid":"https://orcid.org/0000-0003-3586-7969"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Mads Gr\u00e6sb\u00f8ll Christensen","raw_affiliation_strings":["Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066967599","display_name":"Mark D. Plumbley","orcid":"https://orcid.org/0000-0002-9708-1075"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mark D. Plumbley","raw_affiliation_strings":["Department of Electronic Engineering, Queen Mary, University of London, Mile End Road, London E1 4NS, UK"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Queen Mary, University of London, Mile End Road, London E1 4NS, UK","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018292103","display_name":"Lars Kai Hansen","orcid":"https://orcid.org/0000-0003-0442-5877"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Lars Kai Hansen","raw_affiliation_strings":["Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800 Lyngby, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800 Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103115969","display_name":"S\u00f8ren Holdt Jensen","orcid":"https://orcid.org/0000-0002-1050-470X"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"S\u00f8ren Holdt Jensen","raw_affiliation_strings":["Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5025879904"],"corresponding_institution_ids":["https://openalex.org/I891191580"],"apc_list":{"value":2100,"currency":"USD","value_usd":2100},"apc_paid":{"value":2100,"currency":"USD","value_usd":2100},"fwci":12.9144,"has_fulltext":true,"cited_by_count":176,"citation_normalized_percentile":{"value":0.99022801,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"2008","issue":null,"first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9871000051498413,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9865000247955322,"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/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.9759930372238159},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7458008527755737},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6778191924095154},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6099185943603516},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5317026376724243},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.46759527921676636},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4505487084388733},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.42816242575645447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39913833141326904},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3807191550731659},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35177934169769287},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2962188720703125},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.13047096133232117},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.075402170419693}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.9759930372238159},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7458008527755737},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6778191924095154},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6099185943603516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5317026376724243},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.46759527921676636},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4505487084388733},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.42816242575645447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39913833141326904},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3807191550731659},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35177934169769287},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2962188720703125},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.13047096133232117},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.075402170419693},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1155/2008/764206","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/764206","pdf_url":"https://downloads.hindawi.com/journals/cin/2008/764206.pdf","source":{"id":"https://openalex.org/S72372694","display_name":"Computational Intelligence and Neuroscience","issn_l":"1687-5265","issn":["1687-5265","1687-5273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Intelligence and Neuroscience","raw_type":"journal-article"},{"id":"pmid:18497868","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/18497868","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":"Computational intelligence and neuroscience","raw_type":null},{"id":"pmh:oai:pure.atira.dk:openaire/fa5b9300-91f6-11dc-8188-000ea68e967b","is_oa":true,"landing_page_url":"https://vbn.aau.dk/da/publications/fa5b9300-91f6-11dc-8188-000ea68e967b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Laurberg, H, Christensen, M G, Plumbley, M D, Hansen, L K & Jensen, S H 2008, 'Theorems on Positive Data : on the Uniqueness of NMF', Computational Intelligence and Neuroscience. https://doi.org/10.1155/2008/764206","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:alma.44SUR_INST:11140075720002346","is_oa":false,"landing_page_url":"http://doi.org/10.1155/2008/764206","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:epubs.surrey.ac.uk:808459","is_oa":false,"landing_page_url":"http://epubs.surrey.ac.uk/808459/1/Theorems%20on%20positive%20data%3A%20on%20the%20uniqueness%20of%20NMF..pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400680","display_name":"Surrey Research Insight Open Access (The University of Surrey)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28290843","host_organization_name":"University of Surrey","host_organization_lineage":["https://openalex.org/I28290843"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:2386872","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/2386872","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Comput Intell Neurosci","raw_type":"Text"},{"id":"pmh:oai:pure.atira.dk:publications/9423cf5a-4d71-4f14-844f-93150ce6cbff","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/9423cf5a-4d71-4f14-844f-93150ce6cbff","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"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":"Lauerberg , H , Christensen , M G , Pumbley , M , Hansen , L K &amp; Jensen , S H 2008 , ' Theorems on Positive Data: On the Uniqueness of NMF ' , Computational Intelligence and Neuroscience , vol. 2008 , 764206 , pp. 10 . https://doi.org/10.1155/2008/764206","raw_type":"article"},{"id":"pmh:oai:qmro.qmul.ac.uk:123456789/1095","is_oa":false,"landing_page_url":"http://qmro.qmul.ac.uk/jspui/handle/123456789/1095","pdf_url":null,"source":{"id":"https://openalex.org/S4306400530","display_name":"Queen Mary Research Online (Queen Mary University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1155/2008/764206","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/764206","pdf_url":"https://downloads.hindawi.com/journals/cin/2008/764206.pdf","source":{"id":"https://openalex.org/S72372694","display_name":"Computational Intelligence and Neuroscience","issn_l":"1687-5265","issn":["1687-5265","1687-5273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Intelligence and Neuroscience","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8199999928474426}],"awards":[{"id":"https://openalex.org/G3461283054","display_name":null,"funder_award_id":"274-06-0521","funder_id":"https://openalex.org/F4320310484","funder_display_name":"Teknologi og Produktion, Det Frie Forskningsr\u00e5d"},{"id":"https://openalex.org/G4593215662","display_name":null,"funder_award_id":"26-02-0092","funder_id":"https://openalex.org/F4320310484","funder_display_name":"Teknologi og Produktion, Det Frie Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320310484","display_name":"Teknologi og Produktion, Det Frie Forskningsr\u00e5d","ror":"https://ror.org/03ge1nb22"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2048687561.pdf","grobid_xml":"https://content.openalex.org/works/W2048687561.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1497354029","https://openalex.org/W1902027874","https://openalex.org/W2003234507","https://openalex.org/W2003994949","https://openalex.org/W2017288758","https://openalex.org/W2094808655","https://openalex.org/W2103375047","https://openalex.org/W2104298926","https://openalex.org/W2118718620","https://openalex.org/W2135029798","https://openalex.org/W2140318696","https://openalex.org/W2156448167","https://openalex.org/W2165594460","https://openalex.org/W2798735774","https://openalex.org/W2798909945","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W34555840"],"abstract_inverted_index":{"We":[0,44],"investigate":[1],"the":[2,20,36,39,63,80],"conditions":[3],"for":[4],"which":[5,16,77],"nonnegative":[6],"matrix":[7,53],"factorization":[8],"(NMF)":[9],"is":[10,22],"unique":[11,25,51,65],"and":[12,41],"introduce":[13],"several":[14,33],"theorems":[15,29,40],"can":[17],"determine":[18],"whether":[19],"decomposition":[21],"in":[23,85],"fact":[24],"or":[26],"not.":[27],"The":[28],"are":[30],"illustrated":[31],"by":[32,54],"examples":[34],"showing":[35],"use":[37,69],"of":[38,49,62,73,79],"their":[42],"limitations.":[43],"have":[45],"shown":[46],"that":[47],"corruption":[48],"a":[50,59,70],"NMF":[52,74,87],"additive":[55],"noise":[56],"leads":[57],"to":[58,75],"noisy":[60],"estimation":[61,90],"noise-free":[64],"solution.":[66],"Finally,":[67],"we":[68],"stochastic":[71],"view":[72],"analyze":[76],"characterization":[78],"underlying":[81],"model":[82],"will":[83],"result":[84],"an":[86],"with":[88],"small":[89],"errors.":[91]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":21},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
