{"id":"https://openalex.org/W1977899734","doi":"https://doi.org/10.1109/tsp.2015.2394443","title":"Sparse Generalized Eigenvalue Problem Via Smooth Optimization","display_name":"Sparse Generalized Eigenvalue Problem Via Smooth Optimization","publication_year":2015,"publication_date":"2015-01-21","ids":{"openalex":"https://openalex.org/W1977899734","doi":"https://doi.org/10.1109/tsp.2015.2394443","mag":"1977899734"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2015.2394443","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2394443","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/1408.6686","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008686458","display_name":"Junxiao Song","orcid":"https://orcid.org/0000-0002-3236-1535"},"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"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Junxiao Song","raw_affiliation_strings":["Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong","[Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong]"],"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"[Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong]","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]}]},{"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"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"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 (HKUST), Hong Kong","[Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong]"],"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"[Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong]","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054606088","display_name":"Daniel P. Palomar","orcid":"https://orcid.org/0000-0001-5250-4874"},"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"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"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 (HKUST), Hong Kong","[Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong]"],"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"[Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong Kong]","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008686458"],"corresponding_institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":8.0408,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.98014165,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"63","issue":"7","first_page":"1627","last_page":"1642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.672431468963623},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6411871910095215},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6299538016319275},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5277417302131653},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45490559935569763},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4496158957481384},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4482807517051697},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4353005886077881},{"id":"https://openalex.org/keywords/generalized-eigenvector","display_name":"Generalized eigenvector","score":0.4247279167175293},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4198130965232849},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.2814256548881531}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.672431468963623},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6411871910095215},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6299538016319275},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5277417302131653},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45490559935569763},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4496158957481384},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4482807517051697},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4353005886077881},{"id":"https://openalex.org/C147925508","wikidata":"https://www.wikidata.org/wiki/Q970767","display_name":"Generalized eigenvector","level":5,"score":0.4247279167175293},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4198130965232849},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2814256548881531},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"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":5,"locations":[{"id":"doi:10.1109/tsp.2015.2394443","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2394443","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:1408.6686","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1408.6686","pdf_url":"https://arxiv.org/pdf/1408.6686","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:CiteSeerX.psu:10.1.1.758.2837","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.758.2837","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1408.6686.pdf","raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-68018","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-68018","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:1783.1-68018","is_oa":false,"landing_page_url":"http://www.scopus.com/record/display.url?eid=2-s2.0-84924345988&origin=inward","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:1408.6686","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1408.6686","pdf_url":"https://arxiv.org/pdf/1408.6686","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":[{"id":"https://metadata.un.org/sdg/16","score":0.4399999976158142,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1519979896","https://openalex.org/W1522512418","https://openalex.org/W1947741949","https://openalex.org/W1974661392","https://openalex.org/W1975377467","https://openalex.org/W1975900269","https://openalex.org/W1979817396","https://openalex.org/W2012769612","https://openalex.org/W2023722580","https://openalex.org/W2044809283","https://openalex.org/W2047093656","https://openalex.org/W2050551672","https://openalex.org/W2050968963","https://openalex.org/W2056898645","https://openalex.org/W2058451329","https://openalex.org/W2068861059","https://openalex.org/W2097417531","https://openalex.org/W2098290597","https://openalex.org/W2107861471","https://openalex.org/W2122315118","https://openalex.org/W2122744491","https://openalex.org/W2128757878","https://openalex.org/W2143163931","https://openalex.org/W2148694408","https://openalex.org/W2149414429","https://openalex.org/W2167732364","https://openalex.org/W2168745297","https://openalex.org/W2171270653","https://openalex.org/W2615253071","https://openalex.org/W3014542904","https://openalex.org/W3124114587","https://openalex.org/W4230094279","https://openalex.org/W4237723258","https://openalex.org/W4250857377"],"related_works":["https://openalex.org/W1978572805","https://openalex.org/W2020990755","https://openalex.org/W3036464408","https://openalex.org/W3169007055","https://openalex.org/W2377851227","https://openalex.org/W4293088966","https://openalex.org/W1854082044","https://openalex.org/W2366868484","https://openalex.org/W2917463375","https://openalex.org/W2155219672"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,55],"consider":[4],"an":[5,70],"\u2113":[6,59],"<sub":[7,60],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,61],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[9,62],"-norm":[10,63],"penalized":[11],"formulation":[12,32],"of":[13,27,35,168],"the":[14,22,53,58,77,103,120,133,158],"generalized":[15,25,93,105],"eigenvalue":[16,94],"problem":[17],"(GEP),":[18],"aimed":[19],"at":[20,86,149],"extracting":[21],"leading":[23,104],"sparse":[24,138],"eigenvector":[26,106],"a":[28,36,42,65,81,91,126,146],"matrix":[29],"pair.":[30],"The":[31],"involves":[33],"maximization":[34],"discontinuous":[37],"nonconcave":[38],"objective":[39],"function":[40,79,128],"over":[41],"nonconvex":[43],"constraint":[44],"set,":[45],"and":[46,171],"is":[47,72,107,115,129],"therefore":[48],"computationally":[49],"intractable.":[50],"To":[51],"tackle":[52],"problem,":[54],"first":[56],"approximate":[57],"by":[64,80],"continuous":[66],"surrogate":[67,78,135],"function.":[68,136],"Then":[69],"algorithm":[71,100],"developed":[73],"via":[74],"iteratively":[75],"majorizing":[76],"quadratic":[82,127],"separable":[83],"function,":[84],"which":[85],"each":[87],"iteration":[88,151],"reduces":[89],"to":[90,117,131],"regular":[92],"problem.":[95],"A":[96,109],"preconditioned":[97],"steepest":[98],"ascent":[99],"for":[101],"finding":[102],"provided.":[108],"systematic":[110],"way":[111],"based":[112],"on":[113],"smoothing":[114],"proposed":[116,159],"deal":[118],"with":[119,140],"\u201csingularity":[121],"issue\u201d":[122],"that":[123,144,157],"arises":[124],"when":[125],"used":[130],"majorize":[132],"nondifferentiable":[134],"For":[137],"GEPs":[139],"special":[141],"structure,":[142],"algorithms":[143,160,165],"admit":[145],"closed-form":[147],"solution":[148],"every":[150],"are":[152],"derived.":[153],"Numerical":[154],"experiments":[155],"show":[156],"match":[161],"or":[162],"outperform":[163],"existing":[164],"in":[166],"terms":[167],"computational":[169],"complexity":[170],"support":[172],"recovery.":[173]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}