{"id":"https://openalex.org/W4405340633","doi":"https://doi.org/10.1080/00207160.2024.2439328","title":"Computing <i>p</i> th root of a transition matrix with a deep unsupervised learning approach","display_name":"Computing <i>p</i> th root of a transition matrix with a deep unsupervised learning approach","publication_year":2024,"publication_date":"2024-12-11","ids":{"openalex":"https://openalex.org/W4405340633","doi":"https://doi.org/10.1080/00207160.2024.2439328"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2024.2439328","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2024.2439328","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/11380/1364689","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115422932","display_name":"Filippo Camellini","orcid":null},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Filippo Camellini","raw_affiliation_strings":["University of Modena and Reggio Emilia","Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Modena, Italy"],"affiliations":[{"raw_affiliation_string":"University of Modena and Reggio Emilia","institution_ids":["https://openalex.org/I122346577"]},{"raw_affiliation_string":"Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Modena, Italy","institution_ids":["https://openalex.org/I122346577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017595816","display_name":"Giorgia Franchini","orcid":"https://orcid.org/0000-0001-9082-8087"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giorgia Franchini","raw_affiliation_strings":["University of Modena and Reggio Emilia","Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Modena, Italy"],"affiliations":[{"raw_affiliation_string":"University of Modena and Reggio Emilia","institution_ids":["https://openalex.org/I122346577"]},{"raw_affiliation_string":"Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Modena, Italy","institution_ids":["https://openalex.org/I122346577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024279313","display_name":"Marco Prato","orcid":"https://orcid.org/0000-0002-7327-3347"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Prato","raw_affiliation_strings":["University of Modena and Reggio Emilia","Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Modena, Italy"],"affiliations":[{"raw_affiliation_string":"University of Modena and Reggio Emilia","institution_ids":["https://openalex.org/I122346577"]},{"raw_affiliation_string":"Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Modena, Italy","institution_ids":["https://openalex.org/I122346577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5115422932"],"corresponding_institution_ids":["https://openalex.org/I122346577"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23880522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"102","issue":"4","first_page":"577","last_page":"594"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9958000183105469,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9958000183105469,"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"}},{"id":"https://openalex.org/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9829000234603882,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.707197368144989},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.5880898237228394},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.5686038732528687},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5622367858886719},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5232702493667603},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.510639488697052},{"id":"https://openalex.org/keywords/transition","display_name":"Transition (genetics)","score":0.4699901342391968},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.44721555709838867},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.43587011098861694},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4311993718147278},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42784467339515686},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.42609816789627075},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.3918396830558777},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38188478350639343},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3337758779525757}],"concepts":[{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.707197368144989},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.5880898237228394},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.5686038732528687},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5622367858886719},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5232702493667603},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.510639488697052},{"id":"https://openalex.org/C194232998","wikidata":"https://www.wikidata.org/wiki/Q1606712","display_name":"Transition (genetics)","level":3,"score":0.4699901342391968},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44721555709838867},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.43587011098861694},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4311993718147278},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42784467339515686},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.42609816789627075},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3918396830558777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38188478350639343},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3337758779525757},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160.2024.2439328","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2024.2439328","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:iris.unimore.it:11380/1364689","is_oa":true,"landing_page_url":"https://hdl.handle.net/11380/1364689","pdf_url":null,"source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unimore.it:11380/1364689","is_oa":true,"landing_page_url":"https://hdl.handle.net/11380/1364689","pdf_url":null,"source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"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":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W39607795","https://openalex.org/W1483804921","https://openalex.org/W1651247961","https://openalex.org/W1969811075","https://openalex.org/W2076605490","https://openalex.org/W2086619045","https://openalex.org/W2102790339","https://openalex.org/W2112796928","https://openalex.org/W2118918399","https://openalex.org/W2137923580","https://openalex.org/W2470208019","https://openalex.org/W2511820681","https://openalex.org/W2925918685","https://openalex.org/W2964013315","https://openalex.org/W3023463767","https://openalex.org/W3169893408","https://openalex.org/W4288724477"],"related_works":["https://openalex.org/W2734729804","https://openalex.org/W2015136492","https://openalex.org/W1968612088","https://openalex.org/W2186430569","https://openalex.org/W2364963676","https://openalex.org/W3041997070","https://openalex.org/W2735388074","https://openalex.org/W4388292488","https://openalex.org/W2351194865","https://openalex.org/W3015020757"],"abstract_inverted_index":{"Transition":[0],"matrices":[1,19,43,62,100],"are":[2],"a":[3,11,71,83,87,103,141],"tool":[4],"used":[5,23],"to":[6,41,45,59],"describe":[7],"transition":[8,18,61,99],"probabilities":[9],"of":[10,27,48,82,98,135],"Markovian":[12],"process.":[13],"From":[14,70],"an":[15],"applied":[16],"perspective,":[17,73],"are,":[20],"for":[21,52,63],"example,":[22],"in":[24,120],"the":[25,46,79,136],"fields":[26],"credit":[28],"risk":[29],"modeling":[30,53],"and":[31,65,101],"medical":[32],"decision":[33],"analysis.":[34],"In":[35],"these":[36],"domains,":[37],"it":[38,55],"is":[39,138],"possible":[40],"estimate":[42],"according":[44],"frequency":[47],"data":[49],"observations,":[50],"but":[51],"purposes,":[54],"may":[56],"be":[57],"necessary":[58],"calculate":[60],"shorter":[64],"more":[66],"restricted":[67],"time":[68,131],"intervals.":[69],"mathematical":[72],"this":[74],"requirement":[75],"translates":[76],"into":[77],"calculating":[78],"pth":[80,96],"root":[81,97],"stochastic":[84],"matrix":[85],"through":[86,140],"constrained":[88],"optimization":[89],"problem.":[90],"This":[91],"article":[92],"focuses":[93],"on":[94,145],"computing":[95],"proposes":[102],"novel":[104],"approach":[105],"using":[106],"deep":[107,123],"learning-based":[108],"algorithms,":[109],"particularly":[110],"Convolutional":[111],"Neural":[112],"Networks.":[113],"Comparisons":[114],"with":[115],"traditional":[116],"algorithms":[117],"reveal":[118],"that,":[119],"certain":[121],"contexts,":[122],"learning":[124],"models":[125,137],"offer":[126],"computational":[127],"advantages,":[128],"especially":[129],"regarding":[130],"efficiency.":[132],"The":[133],"applicability":[134],"verified":[139],"case":[142],"study":[143],"built":[144],"Fitch":[146],"Ratings":[147],"data.":[148]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}