{"id":"https://openalex.org/W7131710779","doi":"https://doi.org/10.1007/s41109-026-00776-5","title":"Network reliability analysis by means of generalized matrix learning vector quantization","display_name":"Network reliability analysis by means of generalized matrix learning vector quantization","publication_year":2026,"publication_date":"2026-02-26","ids":{"openalex":"https://openalex.org/W7131710779","doi":"https://doi.org/10.1007/s41109-026-00776-5"},"language":"en","primary_location":{"id":"doi:10.1007/s41109-026-00776-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41109-026-00776-5","pdf_url":null,"source":{"id":"https://openalex.org/S3035517252","display_name":"Applied Network Science","issn_l":"2364-8228","issn":["2364-8228"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Network Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1007/s41109-026-00776-5","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064473834","display_name":"Klaus Dohmen","orcid":"https://orcid.org/0000-0002-8076-4101"},"institutions":[{"id":"https://openalex.org/I116397343","display_name":"Hochschule Mittweida","ror":"https://ror.org/024ga3r86","country_code":"DE","type":"education","lineage":["https://openalex.org/I116397343"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus Dohmen","raw_affiliation_strings":["Department of Mathematics, Mittweida University of Applied Sciences, Technikumplatz 17, Mittweida, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mittweida University of Applied Sciences, Technikumplatz 17, Mittweida, Germany","institution_ids":["https://openalex.org/I116397343"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106165343","display_name":"Mandy Lange-Geisler","orcid":null},"institutions":[{"id":"https://openalex.org/I116397343","display_name":"Hochschule Mittweida","ror":"https://ror.org/024ga3r86","country_code":"DE","type":"education","lineage":["https://openalex.org/I116397343"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Mandy Lange-Geisler","raw_affiliation_strings":["Department of Mathematics, Mittweida University of Applied Sciences, Technikumplatz 17, Mittweida, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mittweida University of Applied Sciences, Technikumplatz 17, Mittweida, Germany","institution_ids":["https://openalex.org/I116397343"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027248793","display_name":"Thomas Villmann","orcid":"https://orcid.org/0000-0001-6725-0141"},"institutions":[{"id":"https://openalex.org/I116397343","display_name":"Hochschule Mittweida","ror":"https://ror.org/024ga3r86","country_code":"DE","type":"education","lineage":["https://openalex.org/I116397343"]},{"id":"https://openalex.org/I4210130450","display_name":"Freiberger Compound Materials (Germany)","ror":"https://ror.org/038f3wn67","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210130450"]},{"id":"https://openalex.org/I61893789","display_name":"TU Bergakademie Freiberg","ror":"https://ror.org/031vc2293","country_code":"DE","type":"education","lineage":["https://openalex.org/I61893789"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Villmann","raw_affiliation_strings":["Department of Mathematics, Mittweida University of Applied Sciences, Technikumplatz 17, Mittweida, Germany","Faculty of Mathematics and Computer Science, Freiberg University of Mining and Technology, Akademiestra\u00dfe 6, Freiberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mittweida University of Applied Sciences, Technikumplatz 17, Mittweida, Germany","institution_ids":["https://openalex.org/I116397343"]},{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Freiberg University of Mining and Technology, Akademiestra\u00dfe 6, Freiberg, Germany","institution_ids":["https://openalex.org/I61893789","https://openalex.org/I4210130450"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5106165343"],"corresponding_institution_ids":["https://openalex.org/I116397343"],"apc_list":{"value":790,"currency":"GBP","value_usd":969},"apc_paid":{"value":790,"currency":"GBP","value_usd":969},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3583946,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.19939999282360077,"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"}},"topics":[{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.19939999282360077,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.1923000067472458,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.09430000185966492,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.8586999773979187},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6625999808311462},{"id":"https://openalex.org/keywords/learning-vector-quantization","display_name":"Learning vector quantization","score":0.5945000052452087},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5756000280380249},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4627000093460083},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.46219998598098755},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.45080000162124634},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.43369999527931213}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.8586999773979187},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6625999808311462},{"id":"https://openalex.org/C40567965","wikidata":"https://www.wikidata.org/wiki/Q1820283","display_name":"Learning vector quantization","level":3,"score":0.5945000052452087},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5756000280380249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5296000242233276},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49869999289512634},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4627000093460083},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.46219998598098755},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.45179998874664307},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43230000138282776},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.42590001225471497},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.357699990272522},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33480000495910645},{"id":"https://openalex.org/C83665646","wikidata":"https://www.wikidata.org/wiki/Q42139305","display_name":"Feature vector","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3312000036239624},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s41109-026-00776-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41109-026-00776-5","pdf_url":null,"source":{"id":"https://openalex.org/S3035517252","display_name":"Applied Network Science","issn_l":"2364-8228","issn":["2364-8228"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Network Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4a0c0e3a03df45488a4871e94bc30f28","is_oa":true,"landing_page_url":"https://doaj.org/article/4a0c0e3a03df45488a4871e94bc30f28","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Applied Network Science, Vol 11, Iss 1 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s41109-026-00776-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41109-026-00776-5","pdf_url":null,"source":{"id":"https://openalex.org/S3035517252","display_name":"Applied Network Science","issn_l":"2364-8228","issn":["2364-8228"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Network Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W137482480","https://openalex.org/W139586639","https://openalex.org/W1981567151","https://openalex.org/W1997693398","https://openalex.org/W2016312593","https://openalex.org/W2020746157","https://openalex.org/W2032123850","https://openalex.org/W2039434802","https://openalex.org/W2051671042","https://openalex.org/W2103595817","https://openalex.org/W2167482691","https://openalex.org/W2272817333","https://openalex.org/W3037290570","https://openalex.org/W3081377577","https://openalex.org/W3158142008","https://openalex.org/W4241390638","https://openalex.org/W4245176872","https://openalex.org/W4322754167","https://openalex.org/W4388600699","https://openalex.org/W4401219258"],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,115],"novel":[3],"approach":[4,97],"for":[5,92],"assessing":[6],"the":[7,46,53,59,66,69,112],"reliability":[8,21,61],"of":[9,23,55,68,114,117,121],"error-prone":[10],"systems":[11,104],"and":[12,30,85,105,127],"networks":[13,32],"using":[14,35],"an":[15],"interpretable":[16],"prototype-based":[17],"classification":[18],"framework.":[19],"Specifically,":[20],"levels":[22],"consecutive":[24],"k-out-of-n":[25],"success":[26],"systems,":[27],"failure":[28],"networks,":[29],"domination":[31],"are":[33,90],"classified":[34],"Generalized":[36],"Matrix":[37],"Learning":[38],"Vector":[39],"Quantization":[40],"(GMLVQ).":[41],"Beyond":[42],"achieving":[43],"accurate":[44],"classification,":[45],"proposed":[47,96],"method":[48],"provides":[49],"informative":[50],"insights":[51],"into":[52],"influence":[54],"input":[56],"probabilities":[57],"on":[58,124],"resulting":[60],"levels.":[62],"To":[63],"further":[64,108],"enhance":[65],"interpretability":[67],"learned":[70],"relevance":[71],"matrix":[72],"in":[73],"GMLVQ,":[74],"we":[75],"introduce":[76],"two":[77],"graph-based":[78],"visualization":[79],"strategies":[80],"that":[81,89],"reveal":[82],"structural":[83],"patterns":[84],"relevant":[86],"feature":[87],"interactions":[88],"critical":[91],"reliability-level":[93],"classification.":[94],"The":[95],"is":[98],"generally":[99],"applicable":[100],"to":[101,110],"arbitrary":[102],"coherent":[103],"can":[106],"be":[107],"adapted":[109],"estimate":[111],"probability":[113],"union":[116],"any":[118],"finite":[119],"family":[120],"events":[122],"based":[123],"their":[125],"individual":[126],"pairwise":[128],"intersection":[129],"probabilities.":[130]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2026-02-27T00:00:00"}