{"id":"https://openalex.org/W3000084948","doi":"https://doi.org/10.3390/e22010082","title":"High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality","display_name":"High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality","publication_year":2020,"publication_date":"2020-01-09","ids":{"openalex":"https://openalex.org/W3000084948","doi":"https://doi.org/10.3390/e22010082","mag":"3000084948","pmid":"https://pubmed.ncbi.nlm.nih.gov/33285855"},"language":"en","primary_location":{"id":"doi:10.3390/e22010082","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22010082","pdf_url":"https://www.mdpi.com/1099-4300/22/1/82/pdf?version=1578909469","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/22/1/82/pdf?version=1578909469","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Alexander N. Gorban","orcid":"https://orcid.org/0000-0001-6224-1430"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]},{"id":"https://openalex.org/I79563041","display_name":"N. I. Lobachevsky State University of Nizhny Novgorod","ror":"https://ror.org/01bb1zm18","country_code":"RU","type":"education","lineage":["https://openalex.org/I79563041"]}],"countries":["GB","RU"],"is_corresponding":true,"raw_author_name":"Alexander N. Gorban","raw_affiliation_strings":["Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK","Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, 603022 Nizhny Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, 603022 Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I79563041"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Valery A. Makarov","orcid":"https://orcid.org/0000-0001-8789-7532"},"institutions":[{"id":"https://openalex.org/I79563041","display_name":"N. I. Lobachevsky State University of Nizhny Novgorod","ror":"https://ror.org/01bb1zm18","country_code":"RU","type":"education","lineage":["https://openalex.org/I79563041"]},{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES","RU"],"is_corresponding":false,"raw_author_name":"Valery A. Makarov","raw_affiliation_strings":["Instituto de Matem\u00e1tica Interdisciplinar, Faculty of Mathematics, Universidad Complutense de Madrid, Avda Complutense s/n, 28040 Madrid, Spain","Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, 603022 Nizhny Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica Interdisciplinar, Faculty of Mathematics, Universidad Complutense de Madrid, Avda Complutense s/n, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]},{"raw_affiliation_string":"Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, 603022 Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I79563041"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ivan Y. Tyukin","orcid":"https://orcid.org/0000-0002-7359-7966"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]},{"id":"https://openalex.org/I79563041","display_name":"N. I. Lobachevsky State University of Nizhny Novgorod","ror":"https://ror.org/01bb1zm18","country_code":"RU","type":"education","lineage":["https://openalex.org/I79563041"]}],"countries":["GB","RU"],"is_corresponding":false,"raw_author_name":"Ivan Y. Tyukin","raw_affiliation_strings":["Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK","Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, 603022 Nizhny Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, 603022 Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I79563041"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I153648349","https://openalex.org/I79563041"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.5261,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.93282517,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"22","issue":"1","first_page":"82","last_page":"82"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.20229999721050262,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.20229999721050262,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.06560000032186508,"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/T10320","display_name":"Neural Networks and Applications","score":0.0625,"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/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.8228999972343445},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.772599995136261},{"id":"https://openalex.org/keywords/blessing","display_name":"Blessing","score":0.7595000267028809},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.558899998664856},{"id":"https://openalex.org/keywords/phenomenon","display_name":"Phenomenon","score":0.5449000000953674},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.41519999504089355},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.34299999475479126}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.8228999972343445},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.772599995136261},{"id":"https://openalex.org/C2776195157","wikidata":"https://www.wikidata.org/wiki/Q626510","display_name":"Blessing","level":2,"score":0.7595000267028809},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6881999969482422},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6337000131607056},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.558899998664856},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.5449000000953674},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4113999903202057},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3547999858856201},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C30732413","wikidata":"https://www.wikidata.org/wiki/Q17092636","display_name":"Intrinsic dimension","level":3,"score":0.3012999892234802},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2651999890804291},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C2780273121","wikidata":"https://www.wikidata.org/wiki/Q109411","display_name":"Curse","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25060001015663147}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e22010082","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22010082","pdf_url":"https://www.mdpi.com/1099-4300/22/1/82/pdf?version=1578909469","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":"pmid:33285855","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33285855","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:arXiv.org:2001.04959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.04959","pdf_url":"https://arxiv.org/pdf/2001.04959","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:265b95758a8343eba8a3798435ba6112","is_oa":true,"landing_page_url":"https://doaj.org/article/265b95758a8343eba8a3798435ba6112","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 22, Iss 1, p 82 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/22/1/82/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e22010082","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7516518","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7516518","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e22010082","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22010082","pdf_url":"https://www.mdpi.com/1099-4300/22/1/82/pdf?version=1578909469","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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000084948.pdf","grobid_xml":"https://content.openalex.org/works/W3000084948.grobid-xml"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W231970315","https://openalex.org/W568124517","https://openalex.org/W1573820523","https://openalex.org/W1612304093","https://openalex.org/W1672197616","https://openalex.org/W1786513448","https://openalex.org/W1976301604","https://openalex.org/W1980516134","https://openalex.org/W1987698418","https://openalex.org/W1989274820","https://openalex.org/W1998025025","https://openalex.org/W2001619934","https://openalex.org/W2011058684","https://openalex.org/W2013239224","https://openalex.org/W2027392196","https://openalex.org/W2027625319","https://openalex.org/W2036843111","https://openalex.org/W2045727885","https://openalex.org/W2053826724","https://openalex.org/W2057074619","https://openalex.org/W2078529082","https://openalex.org/W2088658556","https://openalex.org/W2096185893","https://openalex.org/W2101295242","https://openalex.org/W2114588272","https://openalex.org/W2144006746","https://openalex.org/W2146453955","https://openalex.org/W2147344735","https://openalex.org/W2157267184","https://openalex.org/W2160159283","https://openalex.org/W2341365829","https://openalex.org/W2344260814","https://openalex.org/W2516041031","https://openalex.org/W2522853862","https://openalex.org/W2527796832","https://openalex.org/W2541455433","https://openalex.org/W2593455419","https://openalex.org/W2765508388","https://openalex.org/W2784010521","https://openalex.org/W2884716758","https://openalex.org/W2887446625","https://openalex.org/W2892053535","https://openalex.org/W2896466118","https://openalex.org/W2914413333","https://openalex.org/W2919445000","https://openalex.org/W2920567444","https://openalex.org/W2922091614","https://openalex.org/W2923495523","https://openalex.org/W2942330253","https://openalex.org/W2946264462","https://openalex.org/W2952773203","https://openalex.org/W2954559185","https://openalex.org/W2962852687","https://openalex.org/W2977408054","https://openalex.org/W2977585004","https://openalex.org/W2977886961","https://openalex.org/W2979001048","https://openalex.org/W3023991311","https://openalex.org/W3124950027","https://openalex.org/W4239048948","https://openalex.org/W4250954493","https://openalex.org/W4250955649","https://openalex.org/W6633044140","https://openalex.org/W6737910490","https://openalex.org/W6991181077"],"related_works":[],"abstract_inverted_index":{"High-dimensional":[0],"data":[1],"and":[2,15,72,89,96,104],"high-dimensional":[3,57],"representations":[4],"of":[5,10,17,23,26,41,46,85,94],"reality":[6],"are":[7],"inherent":[8],"features":[9],"modern":[11],"Artificial":[12],"Intelligence":[13],"systems":[14],"applications":[16],"machine":[18,102],"learning.":[19],"The":[20],"well-known":[21],"phenomenon":[22],"the":[24,38,42,44,92],"\"curse":[25],"dimensionality\"":[27],"states:":[28],"many":[29],"problems":[30],"become":[31],"exponentially":[32],"difficult":[33],"in":[34,74],"high":[35,75],"dimensions.":[36],"Recently,":[37],"other":[39],"side":[40],"coin,":[43],"\"blessing":[45],"dimensionality\",":[47],"has":[48],"attracted":[49],"much":[50],"attention.":[51],"It":[52],"turns":[53],"out":[54],"that":[55],"generic":[56],"datasets":[58],"exhibit":[59],"fairly":[60],"simple":[61],"geometric":[62],"properties.":[63],"Thus,":[64],"there":[65],"is":[66],"a":[67,81],"fundamental":[68],"tradeoff":[69],"between":[70],"complexity":[71],"simplicity":[73],"dimensional":[76],"spaces.":[77],"Here":[78],"we":[79],"present":[80],"brief":[82],"explanatory":[83],"review":[84],"recent":[86],"ideas,":[87],"results":[88],"hypotheses":[90],"about":[91],"blessing":[93],"dimensionality":[95],"related":[97],"simplifying":[98],"effects":[99],"relevant":[100],"to":[101],"learning":[103],"neuroscience.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":9}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-01-23T00:00:00"}
