{"id":"https://openalex.org/W2054542173","doi":"https://doi.org/10.1002/1520-684x(200008)31:9<28::aid-scj4>3.0.co;2-v","title":"A quadratic discriminant function based on bias rectification of eigenvalues","display_name":"A quadratic discriminant function based on bias rectification of eigenvalues","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2054542173","doi":"https://doi.org/10.1002/1520-684x(200008)31:9<28::aid-scj4>3.0.co;2-v","mag":"2054542173"},"language":"en","primary_location":{"id":"doi:10.1002/1520-684x(200008)31:9<28::aid-scj4>3.0.co;2-v","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1520-684x(200008)31:9<28::aid-scj4>3.0.co;2-v","pdf_url":null,"source":{"id":"https://openalex.org/S58208175","display_name":"Systems and Computers in Japan","issn_l":"0882-1666","issn":["0882-1666","1520-684X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems and Computers in Japan","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/A5076975020","display_name":"Mitsuru Sakai","orcid":null},"institutions":[{"id":"https://openalex.org/I42766147","display_name":"University of Toyama","ror":"https://ror.org/0445phv87","country_code":"JP","type":"education","lineage":["https://openalex.org/I42766147"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mitsuru Sakai","raw_affiliation_strings":["Faculty of Engineering, Toyama University, Toyama, Japan 930-8555","Faculty of Engineering, Toyama University, Toyama, Japan 930\u20108555"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Toyama University, Toyama, Japan 930-8555","institution_ids":["https://openalex.org/I42766147"]},{"raw_affiliation_string":"Faculty of Engineering, Toyama University, Toyama, Japan 930\u20108555","institution_ids":["https://openalex.org/I42766147"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085703375","display_name":"Masaaki Yoneda","orcid":null},"institutions":[{"id":"https://openalex.org/I42766147","display_name":"University of Toyama","ror":"https://ror.org/0445phv87","country_code":"JP","type":"education","lineage":["https://openalex.org/I42766147"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masaaki Yoneda","raw_affiliation_strings":["Faculty of Engineering, Toyama University, Toyama, Japan 930-8555","Faculty of Engineering, Toyama University, Toyama, Japan 930\u20108555"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Toyama University, Toyama, Japan 930-8555","institution_ids":["https://openalex.org/I42766147"]},{"raw_affiliation_string":"Faculty of Engineering, Toyama University, Toyama, Japan 930\u20108555","institution_ids":["https://openalex.org/I42766147"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109167250","display_name":"Hiroyuki Hase","orcid":null},"institutions":[{"id":"https://openalex.org/I42766147","display_name":"University of Toyama","ror":"https://ror.org/0445phv87","country_code":"JP","type":"education","lineage":["https://openalex.org/I42766147"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroyuki Hase","raw_affiliation_strings":["Faculty of Engineering, Toyama University, Toyama, Japan 930-8555","Faculty of Engineering, Toyama University, Toyama, Japan 930\u20108555"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Toyama University, Toyama, Japan 930-8555","institution_ids":["https://openalex.org/I42766147"]},{"raw_affiliation_string":"Faculty of Engineering, Toyama University, Toyama, Japan 930\u20108555","institution_ids":["https://openalex.org/I42766147"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063280077","display_name":"Hiroshi Maruyama","orcid":"https://orcid.org/0000-0001-7100-5800"},"institutions":[{"id":"https://openalex.org/I42766147","display_name":"University of Toyama","ror":"https://ror.org/0445phv87","country_code":"JP","type":"education","lineage":["https://openalex.org/I42766147"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroshi Maruyama","raw_affiliation_strings":["Faculty of Engineering, Toyama University, Toyama, Japan 930-8555","Faculty of Engineering, Toyama University, Toyama, Japan 930\u20108555"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Toyama University, Toyama, Japan 930-8555","institution_ids":["https://openalex.org/I42766147"]},{"raw_affiliation_string":"Faculty of Engineering, Toyama University, Toyama, Japan 930\u20108555","institution_ids":["https://openalex.org/I42766147"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020934485","display_name":"Michiko Naoe","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michiko Naoe","raw_affiliation_strings":["Tateyama System Laboratory Co., Ltd., Toyama, Japan 930-0004","Tateyama System Laboratory Co., Ltd., Toyama, Japan 930\u20100004"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tateyama System Laboratory Co., Ltd., Toyama, Japan 930-0004","institution_ids":[]},{"raw_affiliation_string":"Tateyama System Laboratory Co., Ltd., Toyama, Japan 930\u20100004","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4655,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67179334,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"9","first_page":"28","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9891999959945679,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9891999959945679,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9889000058174133,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8486122488975525},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7095011472702026},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.6609088182449341},{"id":"https://openalex.org/keywords/linear-discriminant-analysis","display_name":"Linear discriminant analysis","score":0.5472878217697144},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.543585479259491},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5324790477752686},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.462340772151947},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4513850808143616},{"id":"https://openalex.org/keywords/discriminant-function-analysis","display_name":"Discriminant function analysis","score":0.4493945240974426},{"id":"https://openalex.org/keywords/sample-mean-and-sample-covariance","display_name":"Sample mean and sample covariance","score":0.4492555260658264},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.41880834102630615},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.36174339056015015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14677059650421143},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11660975217819214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09894758462905884},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05249810218811035}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8486122488975525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7095011472702026},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.6609088182449341},{"id":"https://openalex.org/C69738355","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Linear discriminant analysis","level":2,"score":0.5472878217697144},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.543585479259491},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5324790477752686},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.462340772151947},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4513850808143616},{"id":"https://openalex.org/C41771347","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Discriminant function analysis","level":2,"score":0.4493945240974426},{"id":"https://openalex.org/C181243257","wikidata":"https://www.wikidata.org/wiki/Q1693522","display_name":"Sample mean and sample covariance","level":3,"score":0.4492555260658264},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.41880834102630615},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.36174339056015015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14677059650421143},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11660975217819214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09894758462905884},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05249810218811035},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"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:10.1002/1520-684x(200008)31:9<28::aid-scj4>3.0.co;2-v","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1520-684x(200008)31:9<28::aid-scj4>3.0.co;2-v","pdf_url":null,"source":{"id":"https://openalex.org/S58208175","display_name":"Systems and Computers in Japan","issn_l":"0882-1666","issn":["0882-1666","1520-684X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems and Computers in Japan","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.75,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1482278494","https://openalex.org/W1584444527","https://openalex.org/W1964312039","https://openalex.org/W2040193698","https://openalex.org/W2046649434","https://openalex.org/W2071346966","https://openalex.org/W2129476886","https://openalex.org/W2135346934","https://openalex.org/W2145745009","https://openalex.org/W2165918462","https://openalex.org/W2490800645","https://openalex.org/W6634927326","https://openalex.org/W6679986405"],"related_works":["https://openalex.org/W2146026567","https://openalex.org/W2075660794","https://openalex.org/W1997987234","https://openalex.org/W2167334622","https://openalex.org/W2013111745","https://openalex.org/W4238888834","https://openalex.org/W2392907906","https://openalex.org/W4387528765","https://openalex.org/W2042632150","https://openalex.org/W1964346966"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,14,80,99],"new":[3],"quadratic":[4],"discriminant":[5,86],"function.":[6],"First,":[7],"we":[8,23,48,77],"show":[9,78],"that":[10,84],"the":[11,33,40,50,53,59,96],"eigenvalues":[12,44,56,71],"of":[13,52,98],"covariance":[15],"matrix":[16],"obtained":[17],"from":[18],"samples":[19],"are":[20],"biased.":[21],"Then,":[22],"describe":[24],"how":[25,30],"to":[26,31,38,68],"rectify":[27,69],"them":[28],"and":[29,45,62],"use":[32],"rectified":[34],"eigenvalues.":[35],"In":[36],"order":[37],"derive":[39],"relation":[41],"between":[42],"sample":[43,55,70,101],"true":[46],"eigenvalues,":[47],"analyze":[49],"biases":[51],"expected":[54],"by":[57,79],"using":[58],"perturbation":[60],"method":[61,83],"obtain":[63],"approximate":[64],"simultaneous":[65],"linear":[66],"equations":[67],"in":[72,90,95],"multidimensional":[73],"normal":[74,92],"cases.":[75],"Finally,":[76],"Monte":[81],"Carlo":[82],"our":[85],"function":[87],"works":[88],"effectively":[89],"eight-dimensional":[91],"cases":[93],"especially":[94],"case":[97],"small":[100],"size.":[102],"\u00a9":[103],"2000":[104,112],"Scripta":[105],"Technica,":[106],"Syst":[107],"Comp":[108],"Jpn,":[109],"31(9):":[110],"28\u201338,":[111]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}