{"id":"https://openalex.org/W2920871663","doi":null,"title":"Hebbian learning approaches based on general inner products and distance measures in non-Euclidean spaces","display_name":"Hebbian learning approaches based on general inner products and distance measures in non-Euclidean spaces","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2920871663","mag":"2920871663"},"language":"en","primary_location":{"id":"pmh:oai:pure.rug.nl:openaire/b9886e55-a1b2-445d-8cbb-bb486941faf1","doi":null,"is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/b9886e55-a1b2-445d-8cbb-bb486941faf1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lange, M 2019, 'Hebbian learning approaches based on general inner products and distance measures in non-Euclidean spaces', Doctor of Philosophy, University of Groningen, [Groningen].","raw_type":"info:eu-repo/semantics/doctoralThesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/b9886e55-a1b2-445d-8cbb-bb486941faf1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074111890","display_name":"Mandy Lange","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mandy Lange","raw_affiliation_strings":["Intelligent Systems"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligent Systems","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5074111890"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9945999979972839,"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/T10320","display_name":"Neural Networks and Applications","score":0.9945999979972839,"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/T12676","display_name":"Machine Learning and ELM","score":0.001500000013038516,"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/T13373","display_name":"Data Mining and Machine Learning Applications","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/hebbian-learning","display_name":"Hebbian learning","score":0.9990000128746033},{"id":"https://openalex.org/keywords/semi-inner-products","display_name":"semi-inner products","score":0.8349999785423279},{"id":"https://openalex.org/keywords/banach-spaces","display_name":"Banach spaces","score":0.847000002861023},{"id":"https://openalex.org/keywords/non-euclidean-spaces","display_name":"non-Euclidean spaces","score":0.9110000133514404},{"id":"https://openalex.org/keywords/distance-metrics","display_name":"distance measures","score":0.7350000143051147},{"id":"https://openalex.org/keywords/learning-vector-quantization","display_name":"learning vector quantization","score":0.8859999775886536},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"unsupervised learning","score":0.847000002861023},{"id":"https://openalex.org/keywords/supervised-learning","display_name":"supervised learning","score":0.949999988079071},{"id":"https://openalex.org/keywords/matrix-valued-data","display_name":"matrix-valued data","score":0.8149999976158142},{"id":"https://openalex.org/keywords/matrix-norms","display_name":"matrix norms","score":0.7519999742507935},{"id":"https://openalex.org/keywords/classification","display_name":"classification","score":0.5440000295639038}],"concepts":[{"id":"https://openalex.org/C40567965","wikidata":"https://www.wikidata.org/wiki/Q1820283","display_name":"Learning vector quantization","level":3,"score":0.7709949016571045},{"id":"https://openalex.org/C111437709","wikidata":"https://www.wikidata.org/wiki/Q1277874","display_name":"Hebbian theory","level":3,"score":0.6316264867782593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6161245703697205},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6076092720031738},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.5669466853141785},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4723286032676697},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.46857213973999023},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.44105178117752075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35178130865097046},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.29608428478240967},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2534022927284241},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23739340901374817},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.138953298330307},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:pure.rug.nl:openaire/b9886e55-a1b2-445d-8cbb-bb486941faf1","doi":null,"is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/b9886e55-a1b2-445d-8cbb-bb486941faf1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lange, M 2019, 'Hebbian learning approaches based on general inner products and distance measures in non-Euclidean spaces', Doctor of Philosophy, University of Groningen, [Groningen].","raw_type":"info:eu-repo/semantics/doctoralThesis"},{"id":"pmh:rug:oai:pure.rug.nl:publications/b9886e55-a1b2-445d-8cbb-bb486941faf1","doi":null,"is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/b9886e55-a1b2-445d-8cbb-bb486941faf1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/doctoralthesis"},{"id":"mag:2920871663","doi":null,"is_oa":false,"landing_page_url":"https://research.rug.nl/en/publications/hebbian-learning-approaches-based-on-general-inner-products-and-d","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/b9886e55-a1b2-445d-8cbb-bb486941faf1","doi":null,"is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/b9886e55-a1b2-445d-8cbb-bb486941faf1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lange, M 2019, 'Hebbian learning approaches based on general inner products and distance measures in non-Euclidean spaces', Doctor of Philosophy, University of Groningen, [Groningen].","raw_type":"info:eu-repo/semantics/doctoralThesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1971062249","https://openalex.org/W1608856054","https://openalex.org/W7028688568","https://openalex.org/W4405811724","https://openalex.org/W4318714985","https://openalex.org/W1578531505","https://openalex.org/W4404886412","https://openalex.org/W7095274481","https://openalex.org/W7099260406","https://openalex.org/W79449126"],"abstract_inverted_index":{"The":[0,152,189],"topic":[1],"of":[2,36,51,70,77,102,145,170,187,191,197,208],"this":[3,84,209],"thesis":[4],"is":[5,33,111,133,166,203],"to":[6,149,199],"define":[7],"a":[8,41,127,167,174],"unified":[9],"and":[10,21],"generalized":[11],"scheme":[12,101],"for":[13,19,80,87,92,114,181],"Hebbian":[14,94,128,155,182],"approaches":[15,180],"in":[16,28,60,116,139,194],"non-Euclidean":[17,136,195],"spaces":[18,75,79,89,196],"unsupervised":[20,93],"supervised":[22,104],"learning.":[23],"This":[24],"can":[25,120,141],"be":[26,121],"realized":[27],"different":[29],"ways.":[30],"One":[31],"possibility":[32],"the":[34,37,48,57,61,99,103,143,163,204],"replacement":[35],"inner":[38,53,71,81],"product":[39,43,54],"by":[40],"semi-inner":[42],"(SIP).":[44],"A":[45],"SIP":[46],"relaxes":[47],"strict":[49],"properties":[50],"an":[52],"but":[55],"preserves":[56],"linear":[58],"aspect":[59],"first":[62],"argument.":[63],"Thus,":[64],"these":[65,192],"SIPs":[66,86],"are":[67,90,158],"natural":[68],"equivalents":[69],"products":[72],"generating":[73],"Banach":[74,88],"instead":[76],"Hilbert":[78],"products.":[82],"In":[83],"work":[85],"considered":[91],"like":[95,129,183],"learning":[96,100,147,156,184],"approaches.":[97,160],"Further,":[98],"Learning":[105],"Vector":[106],"Quantization":[107],"(LVQ)":[108],"network,":[109],"which":[110],"originally":[112],"designed":[113],"applications":[115],"Euclidean":[117,150],"data":[118,164,202],"space,":[119],"interpreted":[122],"under":[123],"specific":[124],"circumstances":[125],"as":[126],"learning,":[130],"too.":[131],"It":[132],"shown":[134],"that,":[135],"metrics":[137],"applied":[138],"LVQ":[140],"improve":[142],"performance":[144],"classification":[146],"compared":[148],"variants.":[151],"previously":[153],"addressed":[154],"methods":[157,185,193],"vectorial":[159],"However,":[161],"if":[162],"space":[165,169],"vector":[168],"matrices":[171,198],"equipped":[172],"with":[173],"respective":[175],"matrix":[176,179,201],"norm,":[177],"then":[178],"become":[186],"interest.":[188],"extension":[190],"process":[200],"last":[205],"main":[206],"point":[207],"thesis.":[210]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-10-03T13:16:28.481748","created_date":"2019-03-22T00:00:00"}