{"id":"https://openalex.org/W2116825956","doi":"https://doi.org/10.1162/089976699300016854","title":"A Stochastic Self-Organizing Map for Proximity Data","display_name":"A Stochastic Self-Organizing Map for Proximity Data","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2116825956","doi":"https://doi.org/10.1162/089976699300016854","mag":"2116825956","pmid":"https://pubmed.ncbi.nlm.nih.gov/9950727"},"language":"en","primary_location":{"id":"doi:10.1162/089976699300016854","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976699300016854","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5051619646","display_name":"Thore Graepel","orcid":"https://orcid.org/0000-0003-3957-0310"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Thore Graepel","raw_affiliation_strings":["Department of Computer Science, Technical University of Berlin, Berlin, Germany","Department of Computer Science, Technical University of Berlin, Berlin, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technical University of Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Department of Computer Science, Technical University of Berlin, Berlin, Germany#TAB#","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103171859","display_name":"Klaus Obermayer","orcid":"https://orcid.org/0000-0002-5057-6142"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus Obermayer","raw_affiliation_strings":["Department of Computer Science, Technical University of Berlin, Berlin, Germany","Department of Computer Science, Technical University of Berlin, Berlin, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technical University of Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Department of Computer Science, Technical University of Berlin, Berlin, Germany#TAB#","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051619646"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":null,"apc_paid":null,"fwci":4.4952,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.94706994,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"1","first_page":"139","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9984999895095825,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/self-organizing-map","display_name":"Self-organizing map","score":0.6622501611709595},{"id":"https://openalex.org/keywords/vector-quantization","display_name":"Vector quantization","score":0.654510498046875},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.5565862059593201},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.5440974831581116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5304923057556152},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5219045281410217},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.48024991154670715},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4728532135486603},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.4309900403022766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3624650835990906},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29038408398628235},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.2588631808757782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16583609580993652}],"concepts":[{"id":"https://openalex.org/C111168008","wikidata":"https://www.wikidata.org/wiki/Q1136838","display_name":"Self-organizing map","level":3,"score":0.6622501611709595},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.654510498046875},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.5565862059593201},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5440974831581116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5304923057556152},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5219045281410217},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.48024991154670715},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4728532135486603},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.4309900403022766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3624650835990906},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29038408398628235},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2588631808757782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16583609580993652},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D002415","descriptor_name":"Cats","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D002415","descriptor_name":"Cats","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D002415","descriptor_name":"Cats","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D002540","descriptor_name":"Cerebral Cortex","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D002540","descriptor_name":"Cerebral Cortex","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D002540","descriptor_name":"Cerebral Cortex","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008390","descriptor_name":"Markov Chains","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008390","descriptor_name":"Markov Chains","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008390","descriptor_name":"Markov Chains","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009424","descriptor_name":"Nervous System Physiological Phenomena","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009424","descriptor_name":"Nervous System Physiological Phenomena","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009424","descriptor_name":"Nervous System Physiological Phenomena","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009434","descriptor_name":"Neural Pathways","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009434","descriptor_name":"Neural Pathways","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009434","descriptor_name":"Neural Pathways","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013269","descriptor_name":"Stochastic Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013269","descriptor_name":"Stochastic Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013269","descriptor_name":"Stochastic Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016013","descriptor_name":"Likelihood Functions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016013","descriptor_name":"Likelihood Functions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016013","descriptor_name":"Likelihood Functions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":4,"locations":[{"id":"doi:10.1162/089976699300016854","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976699300016854","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:9950727","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/9950727","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":"Neural computation","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.30.4890","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.4890","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.tu-berlin.de/pub/local/kon/papers/graepel98_tmp_nc.ps.gz","raw_type":"text"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1514609","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/1514609/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   NEURAL COMPUTATION , 11  (1)   pp. 139-155.   (1999)      ","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W23758216","https://openalex.org/W65738273","https://openalex.org/W1504154695","https://openalex.org/W1570862753","https://openalex.org/W1967121925","https://openalex.org/W1975124385","https://openalex.org/W1989470726","https://openalex.org/W1991848143","https://openalex.org/W1999597013","https://openalex.org/W2017117255","https://openalex.org/W2025887562","https://openalex.org/W2032558547","https://openalex.org/W2049633694","https://openalex.org/W2052702017","https://openalex.org/W2074225934","https://openalex.org/W2077990749","https://openalex.org/W2087412702","https://openalex.org/W2100206501","https://openalex.org/W2104163628","https://openalex.org/W2107636931","https://openalex.org/W2108384452","https://openalex.org/W2115305054","https://openalex.org/W2127218421","https://openalex.org/W2134725327","https://openalex.org/W2138996400","https://openalex.org/W2146934815","https://openalex.org/W2148694408","https://openalex.org/W2151689057","https://openalex.org/W2482852864","https://openalex.org/W3017143921","https://openalex.org/W3129711340","https://openalex.org/W4229926969"],"related_works":["https://openalex.org/W2034551444","https://openalex.org/W2023416609","https://openalex.org/W1844640764","https://openalex.org/W2051216975","https://openalex.org/W2982550593","https://openalex.org/W2144077772","https://openalex.org/W2978573861","https://openalex.org/W926742521","https://openalex.org/W2106346348","https://openalex.org/W1534559501"],"abstract_inverted_index":{"We":[0],"derive":[1],"an":[2,17,92,110,127],"efficient":[3],"algorithm":[4,161,169],"for":[5,41,87,136],"topographic":[6,57,101],"mapping":[7],"of":[8,19,37,44,63,69,141,150,159,177,179],"proximity":[9],"data":[10,49],"(TMP),":[11],"which":[12,78,137],"can":[13],"be":[14],"seen":[15],"as":[16],"extension":[18],"Kohonen's":[20],"self-organizing":[21,106],"map":[22,176],"to":[23,97,104,112,121,124,172],"arbitrary":[24],"distance":[25],"measures.":[26],"The":[27],"TMP":[28,113],"cost":[29],"function":[30],"is":[31,76,79,115,134,146,170],"derived":[32],"in":[33,81,130,148],"a":[34,51,60,72,82,174],"Baysian":[35],"framework":[36],"folded":[38],"Markov":[39],"chains":[40],"the":[42,48,56,67,98,105,131,138,142,157,160,164,168,180],"description":[43],"autoencoders.":[45],"It":[46],"incorporates":[47],"by":[50,59],"dissimilarity":[52],"matrix":[53,61],"D":[54,151],"and":[55,152,162],"neighborhood":[58],"H":[62],"transition":[64,99,145],"probabilities.":[65],"From":[66],"principle":[68],"maximum":[70,88],"entropy,":[71],"nonfactorizing":[73],"Gibbs":[74],"distribution":[75],"obtained,":[77],"approximated":[80],"mean-field":[83],"fashion.":[84],"This":[85],"allows":[86],"likelihood":[89],"estimation":[90],"using":[91],"expectation-maximization":[93],"algorithm.":[94],"In":[95,119],"analogy":[96],"from":[100],"vector":[102],"quantization":[103],"map,":[107],"we":[108],"suggest":[109],"approximation":[111],"that":[114],"computationally":[116],"more":[117],"efficient.":[118],"order":[120],"prevent":[122],"convergence":[123],"local":[125],"minima,":[126],"annealing":[128],"scheme":[129],"temperature":[132,140],"parameter":[133],"introduced,":[135],"critical":[139],"first":[143],"phase":[144],"calculated":[147],"terms":[149],"H.":[153],"Numerical":[154],"results":[155],"demonstrate":[156],"working":[158],"confirm":[163],"analytical":[165],"results.":[166],"Finally,":[167],"used":[171],"generate":[173],"connection":[175],"areas":[178],"cat's":[181],"cerebral":[182],"cortex.":[183]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
