{"id":"https://openalex.org/W1502128368","doi":"https://doi.org/10.1109/ijcnn.2005.1556035","title":"Weighted Rayleigh quotients for minor and principal component extraction","display_name":"Weighted Rayleigh quotients for minor and principal component extraction","publication_year":2006,"publication_date":"2006-01-05","ids":{"openalex":"https://openalex.org/W1502128368","doi":"https://doi.org/10.1109/ijcnn.2005.1556035","mag":"1502128368"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2005.1556035","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2005.1556035","pdf_url":null,"source":{"id":"https://openalex.org/S4363609022","display_name":"Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005.","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005.","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/A5063814499","display_name":"M.A. Hasau","orcid":null},"institutions":[{"id":"https://openalex.org/I4210115145","display_name":"University of Minnesota, Duluth","ror":"https://ror.org/01hy4qx27","country_code":"US","type":"education","lineage":["https://openalex.org/I4210115145"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M.A. Hasau","raw_affiliation_strings":["Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN, USA","Dept of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN, USA"],"affiliations":[{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN, USA","institution_ids":["https://openalex.org/I4210115145"]},{"raw_affiliation_string":"Dept of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN, USA","institution_ids":["https://openalex.org/I4210115145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063814499"],"corresponding_institution_ids":["https://openalex.org/I4210115145"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08689249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"1263","last_page":"1268"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9980000257492065,"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/T10057","display_name":"Face and Expression Recognition","score":0.972100019454956,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.8688868284225464},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.7604403495788574},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6991565227508545},{"id":"https://openalex.org/keywords/rayleigh-quotient","display_name":"Rayleigh quotient","score":0.6599256992340088},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6278232932090759},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5599471926689148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5289475917816162},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.508366048336029},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.45351874828338623},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4511335790157318},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4040526747703552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38990354537963867},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37298327684402466},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.37176764011383057},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2948617935180664},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14769533276557922}],"concepts":[{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.8688868284225464},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.7604403495788574},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6991565227508545},{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.6599256992340088},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6278232932090759},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5599471926689148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5289475917816162},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.508366048336029},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.45351874828338623},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4511335790157318},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4040526747703552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38990354537963867},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37298327684402466},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.37176764011383057},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2948617935180664},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14769533276557922},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2005.1556035","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2005.1556035","pdf_url":null,"source":{"id":"https://openalex.org/S4363609022","display_name":"Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005.","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W5731987","https://openalex.org/W1976045444","https://openalex.org/W2006061607","https://openalex.org/W2050583479","https://openalex.org/W2113638573","https://openalex.org/W2114697907","https://openalex.org/W2120206417","https://openalex.org/W2131329059","https://openalex.org/W2133776435","https://openalex.org/W2144689866","https://openalex.org/W2152515657","https://openalex.org/W2160926917","https://openalex.org/W2163335961","https://openalex.org/W2171308192","https://openalex.org/W4210616968"],"related_works":["https://openalex.org/W2368619281","https://openalex.org/W2377143628","https://openalex.org/W2355995962","https://openalex.org/W2392462513","https://openalex.org/W2362718971","https://openalex.org/W2368173763","https://openalex.org/W2977970519","https://openalex.org/W191560551","https://openalex.org/W2075931614","https://openalex.org/W1529452180"],"abstract_inverted_index":{"New":[0],"criteria":[1,85],"are":[2,31,46,72,86],"proposed":[3,23,87,99],"for":[4,88,126],"extracting":[5],"in":[6],"parallel":[7],"multiple":[8,128],"minor":[9,24,63],"and":[10,25,77,80,123],"principal":[11,26,129],"components":[12],"associated":[13],"with":[14],"the":[15,42,48,62,67,92,98,109,112],"covariance":[16,53],"matrix":[17,54],"of":[18,51,56,61,66,82,91,97,111,121],"an":[19,57],"input":[20],"process.":[21],"The":[22],"component":[27,89],"analyzer":[28],"(MCA/PCA)":[29],"algorithms":[30,101,115],"based":[32],"on":[33],"optimizing":[34],"a":[35,52],"weighted":[36],"inverse":[37],"Rayleigh":[38],"quotient":[39],"so":[40],"that":[41],"optimum":[43],"equilibrium":[44],"points":[45],"exactly":[47],"desired":[49],"eigenvectors":[50],"instead":[55],"arbitrary":[58],"orthonormal":[59],"basis":[60],"subspace.":[64],"Variations":[65],"derived":[68],"MCA/PCA":[69],"learning":[70],"rules":[71],"obtained":[73],"by":[74,106],"imposing":[75],"orthogonal":[76],"quadratic":[78],"constraints":[79],"change":[81],"variables.":[83],"Similar":[84],"analysis":[90],"generalized":[93],"eigenvalue":[94],"problem.":[95],"Some":[96],"MCA":[100],"can":[102],"also":[103],"perform":[104],"PCA":[105],"merely":[107],"changing":[108],"sign":[110],"step-size.":[113],"These":[114],"may":[116],"be":[117],"seen":[118],"as":[119],"generalization":[120],"Oja's":[122],"Xu's":[124],"systems":[125],"computing":[127],"components.":[130]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
