{"id":"https://openalex.org/W2110518784","doi":"https://doi.org/10.1109/tpami.2010.186","title":"Accuracy of Pseudo-Inverse Covariance Learning\u2014A Random Matrix Theory Analysis","display_name":"Accuracy of Pseudo-Inverse Covariance Learning\u2014A Random Matrix Theory Analysis","publication_year":2010,"publication_date":"2010-10-19","ids":{"openalex":"https://openalex.org/W2110518784","doi":"https://doi.org/10.1109/tpami.2010.186","mag":"2110518784","pmid":"https://pubmed.ncbi.nlm.nih.gov/20921584"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2010.186","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2010.186","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5014404477","display_name":"David C. Hoyle","orcid":"https://orcid.org/0000-0003-3483-5885"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"D C Hoyle","raw_affiliation_strings":["Faculty of Life Sciences, University of Manchester, Institute of Science and Technology, Manchester, UK","Fac. of Life Sci., Univ. of Manchester, Manchester, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Life Sciences, University of Manchester, Institute of Science and Technology, Manchester, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Fac. of Life Sci., Univ. of Manchester, Manchester, UK","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014404477"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":2.2763,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.89832766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"7","first_page":"1470","last_page":"1481"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9940999746322632,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.984499990940094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.8425376415252686},{"id":"https://openalex.org/keywords/rational-quadratic-covariance-function","display_name":"Rational quadratic covariance function","score":0.8184527158737183},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7376877665519714},{"id":"https://openalex.org/keywords/mat\u00e9rn-covariance-function","display_name":"Mat\u00e9rn covariance function","score":0.7149150371551514},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.6891517639160156},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.677092969417572},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6730573177337646},{"id":"https://openalex.org/keywords/law-of-total-covariance","display_name":"Law of total covariance","score":0.6684221625328064},{"id":"https://openalex.org/keywords/covariance-mapping","display_name":"Covariance mapping","score":0.6011685132980347},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.5436598062515259},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.446969211101532},{"id":"https://openalex.org/keywords/scatter-matrix","display_name":"Scatter matrix","score":0.4286803901195526},{"id":"https://openalex.org/keywords/cma-es","display_name":"CMA-ES","score":0.4239177107810974},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.41457754373550415},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3970467448234558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36731815338134766},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.054427117109298706}],"concepts":[{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.8425376415252686},{"id":"https://openalex.org/C148893098","wikidata":"https://www.wikidata.org/wiki/Q7295778","display_name":"Rational quadratic covariance function","level":5,"score":0.8184527158737183},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7376877665519714},{"id":"https://openalex.org/C118006245","wikidata":"https://www.wikidata.org/wiki/Q6792079","display_name":"Mat\u00e9rn covariance function","level":5,"score":0.7149150371551514},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6891517639160156},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.677092969417572},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6730573177337646},{"id":"https://openalex.org/C126372606","wikidata":"https://www.wikidata.org/wiki/Q6503511","display_name":"Law of total covariance","level":5,"score":0.6684221625328064},{"id":"https://openalex.org/C129759605","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance mapping","level":5,"score":0.6011685132980347},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.5436598062515259},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.446969211101532},{"id":"https://openalex.org/C176917957","wikidata":"https://www.wikidata.org/wiki/Q7430596","display_name":"Scatter matrix","level":4,"score":0.4286803901195526},{"id":"https://openalex.org/C205555498","wikidata":"https://www.wikidata.org/wiki/Q505588","display_name":"CMA-ES","level":4,"score":0.4239177107810974},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.41457754373550415},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3970467448234558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36731815338134766},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.054427117109298706},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2010.186","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2010.186","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:20921584","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20921584","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W20027422","https://openalex.org/W93530381","https://openalex.org/W391578156","https://openalex.org/W1494904807","https://openalex.org/W1520752838","https://openalex.org/W1534201377","https://openalex.org/W1554663460","https://openalex.org/W1964862779","https://openalex.org/W1970763581","https://openalex.org/W1973103003","https://openalex.org/W1974511160","https://openalex.org/W1989132237","https://openalex.org/W1990512452","https://openalex.org/W1992774725","https://openalex.org/W1999772635","https://openalex.org/W2005522417","https://openalex.org/W2006785121","https://openalex.org/W2026988331","https://openalex.org/W2034857737","https://openalex.org/W2038774192","https://openalex.org/W2056532343","https://openalex.org/W2060581589","https://openalex.org/W2066459155","https://openalex.org/W2077733750","https://openalex.org/W2086351984","https://openalex.org/W2095687430","https://openalex.org/W2106084579","https://openalex.org/W2109363337","https://openalex.org/W2117994680","https://openalex.org/W2125027820","https://openalex.org/W2130351130","https://openalex.org/W2133028937","https://openalex.org/W2133743912","https://openalex.org/W2140095548","https://openalex.org/W2157752701","https://openalex.org/W2166381300","https://openalex.org/W2610857016","https://openalex.org/W2912934387","https://openalex.org/W2949734021","https://openalex.org/W2999905431","https://openalex.org/W3101788651","https://openalex.org/W4212883601","https://openalex.org/W4388297464","https://openalex.org/W6629708049","https://openalex.org/W6674279397"],"related_works":["https://openalex.org/W2048777342","https://openalex.org/W4237672998","https://openalex.org/W2110484224","https://openalex.org/W2022823194","https://openalex.org/W4386993326","https://openalex.org/W4281554704","https://openalex.org/W2050026105","https://openalex.org/W4309794518","https://openalex.org/W4311761947","https://openalex.org/W1566386888"],"abstract_inverted_index":{"For":[0,131],"many":[1],"learning":[2],"problems,":[3],"estimates":[4],"of":[5,29,37,81,100,129,151,181],"the":[6,17,27,35,41,50,58,73,82,89,97,101,104,112,121,127,144,170,179,185],"inverse":[7,74,91],"population":[8,75,152],"covariance":[9,19,43,54,64,76,85,92,116,153,188],"are":[10],"required":[11],"and":[12,39,118,140,160,173,197],"often":[13,67],"obtained":[14],"by":[15,111],"inverting":[16],"sample":[18,30,42,53,63,84,115,122,187],"matrix.":[20,77,189],"Increasingly":[21],"for":[22,147],"modern":[23],"scientific":[24],"data":[25,199],"sets,":[26],"number":[28,36,128],"points":[31],"is":[32,44,66,109],"less":[33],"than":[34],"features":[38],"so":[40],"not":[45],"invertible.":[46],"In":[47],"such":[48],"circumstances,":[49],"Moore-Penrose":[51],"pseudo-inverse":[52,83,186],"matrix,":[55],"constructed":[56],"from":[57],"eigenvectors":[59],"corresponding":[60],"to":[61,72,126,142,177],"nonzero":[62,114],"eigenvalues,":[65],"used":[68],"as":[69,120],"an":[70],"approximation":[71],"The":[78,106],"reconstruction":[79,107,145,171],"error":[80,108,146,172],"matrix":[86,137],"in":[87,166,169],"estimating":[88],"true":[90],"can":[93,164,174],"be":[94,175],"quantified":[95],"via":[96],"Frobenius":[98],"norm":[99],"difference":[102],"between":[103],"two.":[105],"dominated":[110],"smallest":[113],"eigenvalues":[117],"diverges":[119],"size":[123],"becomes":[124],"comparable":[125],"features.":[130],"high-dimensional":[132],"data,":[133],"we":[134],"use":[135],"random":[136,161],"theory":[138],"techniques":[139],"results":[141],"study":[143],"a":[148,167],"wide":[149],"class":[150],"matrices.":[154],"We":[155,190],"also":[156],"show":[157],"how":[158],"bagging":[159],"subspace":[162],"methods":[163],"result":[165],"reduction":[168],"combined":[176],"improve":[178],"accuracy":[180],"classifiers":[182],"that":[183],"utilize":[184],"test":[191],"our":[192],"analysis":[193],"on":[194],"both":[195],"simulated":[196],"benchmark":[198],"sets.":[200]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
