{"id":"https://openalex.org/W2032199857","doi":"https://doi.org/10.3390/e14030456","title":"The Mathematical Structure of Information Bottleneck Methods","display_name":"The Mathematical Structure of Information Bottleneck Methods","publication_year":2012,"publication_date":"2012-03-01","ids":{"openalex":"https://openalex.org/W2032199857","doi":"https://doi.org/10.3390/e14030456","mag":"2032199857"},"language":"en","primary_location":{"id":"doi:10.3390/e14030456","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030456","pdf_url":"https://www.mdpi.com/1099-4300/14/3/456/pdf?version=1424784844","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/14/3/456/pdf?version=1424784844","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070531641","display_name":"Tom\u00e1\u0161 Gedeon","orcid":"https://orcid.org/0000-0001-5555-6741"},"institutions":[{"id":"https://openalex.org/I23732399","display_name":"Montana State University","ror":"https://ror.org/02w0trx84","country_code":"US","type":"education","lineage":["https://openalex.org/I23732399","https://openalex.org/I4210126032"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tom\u00e1\u0161 Gedeon","raw_affiliation_strings":["Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA","institution_ids":["https://openalex.org/I23732399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087810451","display_name":"Albert E. Parker","orcid":"https://orcid.org/0000-0002-7994-8624"},"institutions":[{"id":"https://openalex.org/I23732399","display_name":"Montana State University","ror":"https://ror.org/02w0trx84","country_code":"US","type":"education","lineage":["https://openalex.org/I23732399","https://openalex.org/I4210126032"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Albert E. Parker","raw_affiliation_strings":["Center for Biofilm Engineering, Montana State University, Bozeman, MT 59717, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Biofilm Engineering, Montana State University, Bozeman, MT 59717, USA","institution_ids":["https://openalex.org/I23732399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075579436","display_name":"Alexander G. Dimitrov","orcid":"https://orcid.org/0000-0002-8812-3536"},"institutions":[{"id":"https://openalex.org/I137317281","display_name":"Washington State University Vancouver","ror":"https://ror.org/00g2fk805","country_code":"US","type":"education","lineage":["https://openalex.org/I137317281","https://openalex.org/I72951846"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander G. Dimitrov","raw_affiliation_strings":["Department of Mathematics and Science Programs, Washington State University Vancouver, Vancouver, WA 98686, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Science Programs, Washington State University Vancouver, Vancouver, WA 98686, USA","institution_ids":["https://openalex.org/I137317281"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070531641"],"corresponding_institution_ids":["https://openalex.org/I23732399"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.623,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.6977432,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"14","issue":"3","first_page":"456","last_page":"479"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9865000247955322,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9865000247955322,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9469000101089478,"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/information-bottleneck-method","display_name":"Information bottleneck method","score":0.858691930770874},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.6715984344482422},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5831620693206787},{"id":"https://openalex.org/keywords/simulated-annealing","display_name":"Simulated annealing","score":0.5829954147338867},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.488698273897171},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.47771620750427246},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4552761912345886},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4278407096862793},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.42362383008003235},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34464848041534424},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3304887115955353},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3119686543941498}],"concepts":[{"id":"https://openalex.org/C60008888","wikidata":"https://www.wikidata.org/wiki/Q6031013","display_name":"Information bottleneck method","level":3,"score":0.858691930770874},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.6715984344482422},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5831620693206787},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.5829954147338867},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.488698273897171},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.47771620750427246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4552761912345886},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4278407096862793},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.42362383008003235},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34464848041534424},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3304887115955353},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3119686543941498},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e14030456","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030456","pdf_url":"https://www.mdpi.com/1099-4300/14/3/456/pdf?version=1424784844","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:scholarworks.montana.edu:1/12527","is_oa":true,"landing_page_url":"https://scholarworks.montana.edu/handle/1/12527","pdf_url":"https://scholarworks.montana.edu/bitstreams/d5b98d70-a0d6-4aaf-8f17-7b4b3d1b3133/download","source":{"id":"https://openalex.org/S4306402563","display_name":"Montana State University ScholarWorks (Montana State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I23732399","host_organization_name":"Montana State University","host_organization_lineage":["https://openalex.org/I23732399"],"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":"Article"},{"id":"pmh:oai:doaj.org/article:9a37623f21794362ab5ea0ac45fa74c6","is_oa":true,"landing_page_url":"https://doaj.org/article/9a37623f21794362ab5ea0ac45fa74c6","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":"Entropy, Vol 14, Iss 3, Pp 456-479 (2012)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/14/3/456/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e14030456","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy; Volume 14; Issue 3; Pages: 456-479","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e14030456","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030456","pdf_url":"https://www.mdpi.com/1099-4300/14/3/456/pdf?version=1424784844","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[{"id":"https://openalex.org/G4376769336","display_name":"Fluid-Structure Interaction in Arthropod Mechanoreceptors with Application to Bio-Inspired Micro-Fluidic Sensors","funder_award_id":"0849433","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W31389708","https://openalex.org/W1730404227","https://openalex.org/W1965778005","https://openalex.org/W2049872433","https://openalex.org/W2056501338","https://openalex.org/W2063437517","https://openalex.org/W2066784856","https://openalex.org/W2099111195","https://openalex.org/W2103723258","https://openalex.org/W2114290803","https://openalex.org/W2121947440","https://openalex.org/W2127314673","https://openalex.org/W2133604245","https://openalex.org/W2155118599","https://openalex.org/W2161877964","https://openalex.org/W2162111272","https://openalex.org/W2171991173","https://openalex.org/W2979454998","https://openalex.org/W3029645440","https://openalex.org/W3101231107","https://openalex.org/W4213213245","https://openalex.org/W4285719527","https://openalex.org/W4293775970","https://openalex.org/W6601273131","https://openalex.org/W6637108112","https://openalex.org/W6637570865","https://openalex.org/W6679063059"],"related_works":["https://openalex.org/W2939693078","https://openalex.org/W2783047733","https://openalex.org/W3189092450","https://openalex.org/W4287238667","https://openalex.org/W3149287595","https://openalex.org/W2070945723","https://openalex.org/W2920676536","https://openalex.org/W3124771927","https://openalex.org/W3212925274","https://openalex.org/W4225940264"],"abstract_inverted_index":{"Information":[0],"Bottleneck-based":[1],"methods":[2],"use":[3,75,110],"mutual":[4],"information":[5,54],"as":[6],"a":[7,20,38,45],"distortion":[8,55],"function":[9],"in":[10,53,83],"order":[11],"to":[12,30,64,98,118],"extract":[13],"relevant":[14],"details":[15],"about":[16],"the":[17,27,49,78,84,92,99,127,132],"structure":[18],"of":[19,26,51,80,86,101],"complex":[21],"system":[22],"by":[23,36],"compression.":[24],"One":[25],"approaches":[28,109],"used":[29],"generate":[31],"optimal":[32],"compressed":[33],"representations":[34],"is":[35],"annealing":[37,52,66],"parameter.":[39],"In":[40],"this":[41],"manuscript":[42],"we":[43,74,95],"present":[44],"common":[46,63],"framework":[47],"for":[48],"study":[50],"problems.":[56],"We":[57,121],"identify":[58],"features":[59],"that":[60,73],"should":[61],"be":[62,119],"any":[65],"optimization":[67,103],"problem.":[68],"The":[69,107],"main":[70],"mathematical":[71],"tools":[72,137],"come":[76],"from":[77],"analysis":[79],"dynamical":[81],"systems":[82],"presence":[85],"symmetry":[87],"(equivariant":[88],"bifurcation":[89],"theory).":[90],"Through":[91],"compression":[93],"problem,":[94],"make":[96],"connections":[97],"world":[100],"combinatorial":[102],"and":[104,114,138],"pattern":[105],"recognition.":[106],"two":[108,133],"very":[111],"different":[112,116],"vocabularies":[113],"consider":[115],"problems":[117],"\u201cinteresting\u201d.":[120],"provide":[122],"an":[123],"initial":[124],"link,":[125],"through":[126],"Normalized":[128],"Cut":[129],"Problem,":[130],"where":[131],"disciplines":[134],"can":[135],"exchange":[136],"ideas.":[139]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2016-06-24T00:00:00"}