{"id":"https://openalex.org/W1572002268","doi":"https://doi.org/10.1007/978-3-540-30548-4_36","title":"The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints","display_name":"The Solution Space for Fisher Discriminant Analysis and the Uniqueness Under Constraints","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1572002268","doi":"https://doi.org/10.1007/978-3-540-30548-4_36","mag":"1572002268"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-30548-4_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-30548-4_36","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5108050904","display_name":"Wei\u2010Shi Zheng","orcid":"https://orcid.org/0000-0001-8327-0003"},"institutions":[{"id":"https://openalex.org/I142974352","display_name":"National Sun Yat-sen University","ror":"https://ror.org/00mjawt10","country_code":"TW","type":"education","lineage":["https://openalex.org/I142974352"]},{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN","TW"],"is_corresponding":true,"raw_author_name":"Weishi Zheng","raw_affiliation_strings":["Department of Mathematics, Sun Yat-sen University, \u00a0","Department of Mathematics, Sun Yat-sen University,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sun Yat-sen University, \u00a0","institution_ids":["https://openalex.org/I157773358","https://openalex.org/I142974352"]},{"raw_affiliation_string":"Department of Mathematics, Sun Yat-sen University,","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034685928","display_name":"Jianhuang Lai","orcid":"https://orcid.org/0000-0003-3883-2024"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]},{"id":"https://openalex.org/I142974352","display_name":"National Sun Yat-sen University","ror":"https://ror.org/00mjawt10","country_code":"TW","type":"education","lineage":["https://openalex.org/I142974352"]}],"countries":["CN","TW"],"is_corresponding":false,"raw_author_name":"Jianhuang Lai","raw_affiliation_strings":["Department of Mathematics, Sun Yat-sen University, \u00a0","Department of Mathematics, Sun Yat-sen University,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sun Yat-sen University, \u00a0","institution_ids":["https://openalex.org/I157773358","https://openalex.org/I142974352"]},{"raw_affiliation_string":"Department of Mathematics, Sun Yat-sen University,","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079920605","display_name":"Pong C. Yuen","orcid":"https://orcid.org/0000-0002-9343-2202"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"P. C. Yuen","raw_affiliation_strings":["Department of Computer Science, Hong Kong Baptist University, \u00a0","Department of Computer Science Hong Kong Baptist University#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hong Kong Baptist University, \u00a0","institution_ids":["https://openalex.org/I141568987"]},{"raw_affiliation_string":"Department of Computer Science Hong Kong Baptist University#TAB#","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108050904"],"corresponding_institution_ids":["https://openalex.org/I142974352","https://openalex.org/I157773358"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15739023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"313","last_page":"319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9843000173568726,"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"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9843000173568726,"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/T13717","display_name":"Advanced Algorithms and Applications","score":0.9575999975204468,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10320","display_name":"Neural Networks and Applications","score":0.9473999738693237,"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/uniqueness","display_name":"Uniqueness","score":0.6990684270858765},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6814067363739014},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6556015610694885},{"id":"https://openalex.org/keywords/linear-discriminant-analysis","display_name":"Linear discriminant analysis","score":0.6487200260162354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6033164262771606},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5866546630859375},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5127952694892883},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4874558448791504},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.480520099401474},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.466305136680603},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4198288917541504},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3826671540737152},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3728148937225342},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.230075865983963},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10737407207489014},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09985530376434326}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6990684270858765},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6814067363739014},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6556015610694885},{"id":"https://openalex.org/C69738355","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Linear discriminant analysis","level":2,"score":0.6487200260162354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6033164262771606},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5866546630859375},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5127952694892883},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4874558448791504},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.480520099401474},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.466305136680603},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4198288917541504},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3826671540737152},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3728148937225342},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.230075865983963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10737407207489014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09985530376434326},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-30548-4_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-30548-4_36","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1989702938","https://openalex.org/W1991390949","https://openalex.org/W2001619934","https://openalex.org/W2009596443","https://openalex.org/W2023717039","https://openalex.org/W2121647436","https://openalex.org/W2134262590"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W2366107444","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}