{"id":"https://openalex.org/W2978147885","doi":"https://doi.org/10.1109/ijcnn.2019.8852237","title":"On the Linear Separability of Random Points in the d-dimensional Spherical Layer and in the d-dimensional Cube","display_name":"On the Linear Separability of Random Points in the d-dimensional Spherical Layer and in the d-dimensional Cube","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2978147885","doi":"https://doi.org/10.1109/ijcnn.2019.8852237","mag":"2978147885"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2019.8852237","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2019.8852237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"},"type":"article","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/A5040424411","display_name":"Sergey Sidorov","orcid":"https://orcid.org/0000-0003-2883-6427"},"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"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"S. V. Sidorov","raw_affiliation_strings":["Institute of Information Technologies, Mathematics and Mechanics Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Institute of Information Technologies, Mathematics and Mechanics Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia","institution_ids":["https://openalex.org/I79563041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091565051","display_name":"Nikolai Yu. Zolotykh","orcid":"https://orcid.org/0000-0003-4542-9233"},"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"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"N. Yu. Zolotykh","raw_affiliation_strings":["Institute of Information Technologies, Mathematics and Mechanics Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Institute of Information Technologies, Mathematics and Mechanics Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia","institution_ids":["https://openalex.org/I79563041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040424411"],"corresponding_institution_ids":["https://openalex.org/I79563041"],"apc_list":null,"apc_paid":null,"fwci":0.7599,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7042652,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"1","issue":null,"first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9646000266075134,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12417","display_name":"Morphological variations and asymmetry","score":0.9646000266075134,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9613000154495239,"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/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9409000277519226,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.799298882484436},{"id":"https://openalex.org/keywords/layer","display_name":"Layer (electronics)","score":0.6023325324058533},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3757641911506653},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3608248233795166},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32300442457199097},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.17527034878730774},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.09215843677520752}],"concepts":[{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.799298882484436},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.6023325324058533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3757641911506653},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3608248233795166},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32300442457199097},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.17527034878730774},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.09215843677520752}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2019.8852237","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2019.8852237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1971216370","https://openalex.org/W2027392196","https://openalex.org/W2593455419","https://openalex.org/W2793111260","https://openalex.org/W2884716758","https://openalex.org/W6749251518"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"The":[0],"authors":[1],"of":[2,10,44,53,55,62],"[6]":[3],"propose":[4],"a":[5,69,87],"method":[6],"for":[7,37,98],"correcting":[8],"errors":[9],"artificial":[11],"intelligence":[12],"systems":[13],"by":[14,58],"separating":[15],"erroneous":[16],"cases":[17,101],"with":[18,68],"the":[19,28,41,51,60,79,93],"Fisher":[20],"linear":[21],"discriminant.":[22],"It":[23],"turned":[24],"out":[25],"that":[26,64],"if":[27],"dimension":[29],"is":[30],"large":[31],"this":[32,47,56],"approach":[33,57],"works":[34],"well":[35],"even":[36],"an":[38],"exponential":[39],"(of":[40],"dimension)":[42],"number":[43,61],"samples.":[45],"In":[46],"paper,":[48],"we":[49],"specify":[50],"limits":[52],"applicability":[54],"estimating":[59],"points":[63,80],"are":[65],"linearly":[66],"separable":[67],"probability":[70],"close":[71],"to":[72],"1":[73],"in":[74,106],"two":[75,100],"particular":[76],"cases:":[77],"when":[78],"drawn":[81],"randomly,":[82],"independently":[83],"and":[84,91],"uniformly":[85],"from":[86,92],"d-dimensional":[88,94],"spherical":[89],"layer":[90],"cube.":[95],"Our":[96],"bounds":[97,104],"these":[99],"improve":[102],"some":[103],"obtained":[105],"[6].":[107]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
