{"id":"https://openalex.org/W2170615774","doi":"https://doi.org/10.1007/978-3-642-12159-3_10","title":"The Mathematics of Divergence Based Online Learning in Vector Quantization","display_name":"The Mathematics of Divergence Based Online Learning in Vector Quantization","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2170615774","doi":"https://doi.org/10.1007/978-3-642-12159-3_10","mag":"2170615774"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-12159-3_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-12159-3_10","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Thomas Villmann","raw_affiliation_strings":["Department of Mathematics/Natural Sciences/Informatics, University of Applied Sciences Mittweida, 09648, Mittweida, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics/Natural Sciences/Informatics, University of Applied Sciences Mittweida, 09648, Mittweida, Germany","institution_ids":["https://openalex.org/I116397343"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106418987","display_name":"Sven Haase","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":false,"raw_author_name":"Sven Haase","raw_affiliation_strings":["Department of Mathematics/Natural Sciences/Informatics, University of Applied Sciences Mittweida, 09648, Mittweida, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics/Natural Sciences/Informatics, University of Applied Sciences Mittweida, 09648, Mittweida, Germany","institution_ids":["https://openalex.org/I116397343"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004196006","display_name":"Frank-Michael Schleif","orcid":"https://orcid.org/0000-0002-7539-1283"},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank-Michael Schleif","raw_affiliation_strings":["Institute of Computer Science, Clausthal University of Technology, Clausthal-Zellerfeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Clausthal University of Technology, Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091180862","display_name":"Barbara Hammer","orcid":"https://orcid.org/0000-0002-0935-5591"},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Barbara Hammer","raw_affiliation_strings":["Institute of Computer Science, Clausthal University of Technology, Clausthal-Zellerfeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Clausthal University of Technology, Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083548477","display_name":"Michael Biehl","orcid":"https://orcid.org/0000-0001-5148-4568"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Michael Biehl","raw_affiliation_strings":["Johann Bernoulli Inst. for Mathematics and Computer Science, Rijksuniversity Groningen, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Bernoulli Inst. for Mathematics and Computer Science, Rijksuniversity Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027248793"],"corresponding_institution_ids":["https://openalex.org/I116397343"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.0857,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.799921,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"108","last_page":"119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10901","display_name":"Advanced Data Compression Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.9897000193595886,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/learning-vector-quantization","display_name":"Learning vector quantization","score":0.9392714500427246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6671504378318787},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6144481897354126},{"id":"https://openalex.org/keywords/vector-quantization","display_name":"Vector quantization","score":0.6096551418304443},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5592658519744873},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5360292196273804},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5086504220962524},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5068464875221252},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4916902184486389},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.4827410578727722},{"id":"https://openalex.org/keywords/supervised-learning","display_name":"Supervised learning","score":0.4283606708049774},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.42061448097229004},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"Unsupervised learning","score":0.4169471263885498},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.36399656534194946},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2773219645023346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2668570280075073},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.14956459403038025}],"concepts":[{"id":"https://openalex.org/C40567965","wikidata":"https://www.wikidata.org/wiki/Q1820283","display_name":"Learning vector quantization","level":3,"score":0.9392714500427246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6671504378318787},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6144481897354126},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.6096551418304443},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5592658519744873},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5360292196273804},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5086504220962524},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5068464875221252},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4916902184486389},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.4827410578727722},{"id":"https://openalex.org/C136389625","wikidata":"https://www.wikidata.org/wiki/Q334384","display_name":"Supervised learning","level":3,"score":0.4283606708049774},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.42061448097229004},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.4169471263885498},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.36399656534194946},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2773219645023346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2668570280075073},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.14956459403038025},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-642-12159-3_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-12159-3_10","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pub.uni-bielefeld.de:2982116","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2982116","pdf_url":null,"source":{"id":"https://openalex.org/S4306401624","display_name":"Publikationen an der Universit\u00e4t Bielefeld (Universit\u00e4t Bielefeld)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"http://purl.org/coar/resource_type/c_3248"},{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/222b0e64-f98f-4736-b236-12e761fd1a7e","is_oa":false,"landing_page_url":"https://hdl.handle.net/11370/222b0e64-f98f-4736-b236-12e761fd1a7e","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,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Villmann, T, Haase, S, Schleif, F-M, Hammer, B & Biehl, M 2010, The Mathematics of Divergence Based Online Learning in Vector Quantization. in Artificial Neural Networks In Pattern Recognition : Proc. ANNPR 2010. Lecture Notes in Computer Science, vol. 5998, Springer, pp. 108-119. https://doi.org/10.1007/978-3-642-12159-3_10","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:rug:oai:pure.rug.nl:publications/222b0e64-f98f-4736-b236-12e761fd1a7e","is_oa":false,"landing_page_url":"https://research.rug.nl/en/publications/222b0e64-f98f-4736-b236-12e761fd1a7e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Artificial Neural Networks In Pattern Recognition: Proc. ANNPR 2010, 108 - 119","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W30127062","https://openalex.org/W294370321","https://openalex.org/W370143576","https://openalex.org/W1244094129","https://openalex.org/W1246381107","https://openalex.org/W1490200051","https://openalex.org/W1510073064","https://openalex.org/W1510636549","https://openalex.org/W1519208986","https://openalex.org/W1520168181","https://openalex.org/W1538021842","https://openalex.org/W1550888756","https://openalex.org/W1597507633","https://openalex.org/W1624804034","https://openalex.org/W1664167130","https://openalex.org/W1679913846","https://openalex.org/W1965555277","https://openalex.org/W1993646420","https://openalex.org/W2012530888","https://openalex.org/W2019377636","https://openalex.org/W2028125409","https://openalex.org/W2035641621","https://openalex.org/W2039434802","https://openalex.org/W2088068357","https://openalex.org/W2094150678","https://openalex.org/W2096765209","https://openalex.org/W2102108412","https://openalex.org/W2107025582","https://openalex.org/W2119942013","https://openalex.org/W2122882636","https://openalex.org/W2123749980","https://openalex.org/W2134383396","https://openalex.org/W2139094401","https://openalex.org/W2142390010","https://openalex.org/W2166322089","https://openalex.org/W2188078511","https://openalex.org/W2404400936","https://openalex.org/W2515810558","https://openalex.org/W2912554872","https://openalex.org/W2969734899","https://openalex.org/W2977686827","https://openalex.org/W3021971632","https://openalex.org/W3127518054","https://openalex.org/W3137136951","https://openalex.org/W4212918677","https://openalex.org/W4236364574","https://openalex.org/W4237222446","https://openalex.org/W4292156489","https://openalex.org/W4400554083","https://openalex.org/W6831071601"],"related_works":["https://openalex.org/W2100968651","https://openalex.org/W4243803532","https://openalex.org/W1530525041","https://openalex.org/W4244998381","https://openalex.org/W2352648934","https://openalex.org/W4230688072","https://openalex.org/W1915693853","https://openalex.org/W2378212145","https://openalex.org/W2798892016","https://openalex.org/W2202992072"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
