{"id":"https://openalex.org/W2271854708","doi":"https://doi.org/10.1109/tsp.2016.2605073","title":"Orthogonal Sparse PCA and Covariance Estimation via Procrustes Reformulation","display_name":"Orthogonal Sparse PCA and Covariance Estimation via Procrustes Reformulation","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2271854708","doi":"https://doi.org/10.1109/tsp.2016.2605073","mag":"2271854708"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2016.2605073","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2016.2605073","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1602.03992","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046381729","display_name":"Konstantinos Benidis","orcid":"https://orcid.org/0000-0002-0541-6676"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Konstantinos Benidis","raw_affiliation_strings":["Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100672752","display_name":"Ying Sun","orcid":"https://orcid.org/0000-0002-9709-6509"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Ying Sun","raw_affiliation_strings":["Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012466580","display_name":"Prabhu Babu","orcid":"https://orcid.org/0000-0002-9041-9010"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Prabhu Babu","raw_affiliation_strings":["Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054606088","display_name":"Daniel P. Palomar","orcid":null},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Daniel P. Palomar","raw_affiliation_strings":["Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046381729"],"corresponding_institution_ids":["https://openalex.org/I200769079"],"apc_list":null,"apc_paid":null,"fwci":5.9074,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.9628305,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"64","issue":"23","first_page":"6211","last_page":"6226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9957000017166138,"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/T10057","display_name":"Face and Expression Recognition","score":0.9932000041007996,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6275337934494019},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6215453743934631},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.6014758348464966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5996958017349243},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5796906352043152},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.5300103425979614},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4996471405029297},{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.47748705744743347},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.46190932393074036},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4593870937824249},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.4518600404262543},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4468553364276886},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3354499340057373},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.332366943359375},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08070912957191467}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6275337934494019},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6215453743934631},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.6014758348464966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5996958017349243},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5796906352043152},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5300103425979614},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4996471405029297},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.47748705744743347},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.46190932393074036},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4593870937824249},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.4518600404262543},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4468553364276886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3354499340057373},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.332366943359375},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08070912957191467},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2016.2605073","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2016.2605073","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1602.03992","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.03992","pdf_url":"https://arxiv.org/pdf/1602.03992","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-81279","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-81279","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:repository.ust.hk:1783.1-81279","is_oa":false,"landing_page_url":"http://lbdiscover.ust.hk/uresolver?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rfr_id=info:sid/HKUST:SPI&rft.genre=article&rft.issn=1053-587X&rft.volume=0&rft.issue=99&rft.date=2016&rft.spage=&rft.aulast=Benidis&rft.aufirst=K.&rft.atitle=Orthogonal+Sparse+PCA+and+Covariance+Estimation+via+Procrustes+Reformulation&rft.title=IEEE+Transactions+on+Signal+Processing","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1602.03992","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.03992","pdf_url":"https://arxiv.org/pdf/1602.03992","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W1569618673","https://openalex.org/W1947741949","https://openalex.org/W1961876782","https://openalex.org/W1975377467","https://openalex.org/W1975900269","https://openalex.org/W1977899734","https://openalex.org/W1978494516","https://openalex.org/W1998409929","https://openalex.org/W2008049885","https://openalex.org/W2014706477","https://openalex.org/W2044600950","https://openalex.org/W2044809283","https://openalex.org/W2050968963","https://openalex.org/W2057069782","https://openalex.org/W2058451329","https://openalex.org/W2059606882","https://openalex.org/W2062125287","https://openalex.org/W2097417531","https://openalex.org/W2098290597","https://openalex.org/W2098854771","https://openalex.org/W2107861471","https://openalex.org/W2113600901","https://openalex.org/W2130351130","https://openalex.org/W2132555912","https://openalex.org/W2135046866","https://openalex.org/W2137389015","https://openalex.org/W2137404238","https://openalex.org/W2144353980","https://openalex.org/W2144629557","https://openalex.org/W2149414429","https://openalex.org/W2152851576","https://openalex.org/W2156529323","https://openalex.org/W2167732364","https://openalex.org/W2296319761","https://openalex.org/W2402160635","https://openalex.org/W2615253071","https://openalex.org/W2741417216","https://openalex.org/W2950109360","https://openalex.org/W2952736586","https://openalex.org/W2963338452","https://openalex.org/W3014542904","https://openalex.org/W3041093287","https://openalex.org/W3099514962","https://openalex.org/W3101788651","https://openalex.org/W3103917751","https://openalex.org/W3105790468","https://openalex.org/W3124158341","https://openalex.org/W3145074154","https://openalex.org/W4250589301","https://openalex.org/W4285719527","https://openalex.org/W6633980160","https://openalex.org/W6641280533","https://openalex.org/W6680611266","https://openalex.org/W6681309176","https://openalex.org/W6742015047","https://openalex.org/W7075750350"],"related_works":["https://openalex.org/W2022823194","https://openalex.org/W2126916073","https://openalex.org/W1987404909","https://openalex.org/W3211883524","https://openalex.org/W1627656821","https://openalex.org/W2508422113","https://openalex.org/W2018001152","https://openalex.org/W2109377650","https://openalex.org/W2104432942","https://openalex.org/W3025277714"],"abstract_inverted_index":{"The":[0,94,126],"problem":[1,43,95,129,154,177],"of":[2,6,14,35,62,71,118,169,200],"estimating":[3],"sparse":[4,56,87],"eigenvectors":[5,28,88,158],"a":[7,12,22,36,46,55,81,112,134,140,147],"symmetric":[8],"matrix":[9,172],"has":[10,139],"attracted":[11],"lot":[13],"attention":[15],"in":[16,198],"many":[17],"applications,":[18],"especially":[19],"those":[20],"with":[21],"high":[23],"dimensional":[24],"dataset.":[25],"While":[26],"classical":[27],"can":[29],"be":[30,133,162],"obtained":[31],"as":[32],"the":[33,50,59,63,69,73,105,119,123,151,166,170,183,190,207,212],"solution":[34],"maximization":[37,128],"problem,":[38,137],"existing":[39,196],"approaches":[40],"formulate":[41,174],"this":[42,77],"by":[44],"adding":[45],"penalty":[47],"term":[48],"into":[49],"objective":[51,120],"function":[52,121],"that":[53,189],"encourages":[54],"solution.":[57,142],"However,":[58],"vast":[60],"majority":[61],"resulting":[64],"methods":[65],"achieve":[66],"sparsity":[67,181],"at":[68],"expense":[70],"sacrificing":[72],"orthogonality":[74],"property.":[75],"In":[76,143],"paper,":[78],"we":[79,109,145,179],"develop":[80],"new":[82],"method":[83,148],"to":[84,101,132,149,161,173],"estimate":[85],"dominant":[86],"without":[89],"trading":[90],"off":[91],"their":[92],"orthogonality.":[93],"is":[96],"highly":[97],"nonconvex":[98],"and":[99,203],"hard":[100],"handle.":[102],"We":[103,164],"apply":[104],"minorization-maximization":[106],"framework,":[107],"wherein":[108,178],"iteratively":[110],"maximize":[111],"tight":[113],"lower":[114],"bound":[115],"(surrogate":[116],"function)":[117],"over":[122],"Stiefel":[124],"manifold.":[125],"inner":[127],"turns":[130],"out":[131],"rectangular":[135],"Procrustes":[136],"which":[138],"closed-form":[141],"addition,":[144],"propose":[146],"improve":[150,211],"covariance":[152,171,208,214],"estimation":[153,209],"when":[155],"its":[156],"underlying":[157],"are":[159],"known":[160],"sparse.":[163],"use":[165],"eigenvalue":[167],"decomposition":[168],"an":[175],"optimization":[176],"impose":[180],"on":[182],"corresponding":[184],"eigenvectors.":[185],"Numerical":[186],"experiments":[187],"show":[188],"proposed":[191],"eigenvector":[192],"extraction":[193],"algorithm":[194],"outperforms":[195],"algorithms":[197,210],"terms":[199],"support":[201],"recovery":[202],"explained":[204],"variance,":[205],"whereas":[206],"sample":[213],"estimator":[215],"significantly.":[216]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
