{"id":"https://openalex.org/W2022187236","doi":"https://doi.org/10.1137/0202021","title":"Continuous Group Averaging and Pattern Classification Problems","display_name":"Continuous Group Averaging and Pattern Classification Problems","publication_year":1973,"publication_date":"1973-12-01","ids":{"openalex":"https://openalex.org/W2022187236","doi":"https://doi.org/10.1137/0202021","mag":"2022187236"},"language":"en","primary_location":{"id":"doi:10.1137/0202021","is_oa":false,"landing_page_url":"http://doi.org/10.1137/0202021","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-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/A5001889251","display_name":"J. C. Dunn","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. C. Dunn","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001889251"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5785,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.865695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"4","first_page":"253","last_page":"272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.7358999848365784,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.7358999848365784,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.7275000214576721,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.7232999801635742,"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/group","display_name":"Group (periodic table)","score":0.5756725668907166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4082486629486084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3983733057975769},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3784887194633484},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32333338260650635},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1233178973197937}],"concepts":[{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5756725668907166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4082486629486084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3983733057975769},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3784887194633484},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32333338260650635},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1233178973197937},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0202021","is_oa":false,"landing_page_url":"http://doi.org/10.1137/0202021","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W118296737","https://openalex.org/W2083203645","https://openalex.org/W2139794367","https://openalex.org/W3147937051","https://openalex.org/W4214821620"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"The":[0],"relationship":[1],"between":[2],"pattern":[3],"classification":[4,42],"problems":[5],"and":[6,37,78],"the":[7,26,41,47,57,82],"elementary":[8],"theory":[9],"of":[10,28,43,50,61,67],"group":[11,31,60],"invariants":[12,21],"is":[13,32,54],"considered.":[14],"A":[15],"general":[16],"procedure":[17],"for":[18],"obtaining":[19],"quantitative":[20],"by":[22],"averaging":[23],"functionals":[24],"over":[25,56],"manifold":[27],"a":[29,51,65],"continuous":[30,59],"examined":[33],"in":[34,81],"some":[35],"detail,":[36],"then":[38],"applied":[39],"to":[40,63,74],"plane":[44,52],"figures.":[45],"Specifically,":[46],"Fourier":[48],"transform":[49],"figure":[53],"averaged":[55],"one-parameter":[58],"dilatations":[62],"obtain":[64],"pair":[66],"interesting":[68],"scale":[69],"invariant":[70],"transforms":[71],"which":[72],"tend":[73],"pick":[75],"out":[76],"corners":[77],"flat":[79],"spots":[80],"figure\u2019s":[83],"boundary.":[84]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}