{"id":"https://openalex.org/W3182435136","doi":"https://doi.org/10.1109/tnnls.2021.3091598","title":"Low-Rank Plus Sparse Decomposition of Covariance Matrices Using Neural Network Parametrization","display_name":"Low-Rank Plus Sparse Decomposition of Covariance Matrices Using Neural Network Parametrization","publication_year":2021,"publication_date":"2021-07-07","ids":{"openalex":"https://openalex.org/W3182435136","doi":"https://doi.org/10.1109/tnnls.2021.3091598","mag":"3182435136","pmid":"https://pubmed.ncbi.nlm.nih.gov/34232894"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3091598","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1908.00461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081262086","display_name":"Michel Baes","orcid":"https://orcid.org/0000-0001-5482-4556"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"funder","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Michel Baes","raw_affiliation_strings":["Department of Mathematics, RiskLab, ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, RiskLab, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085598326","display_name":"Calypso Herrera","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"funder","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Calypso Herrera","raw_affiliation_strings":["Department of Mathematics, ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010656544","display_name":"Ariel Neufeld","orcid":"https://orcid.org/0000-0001-5500-5245"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"funder","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Ariel Neufeld","raw_affiliation_strings":["Division of Mathematical Sciences, NTU Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, NTU Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020689635","display_name":"Pierre Ruyssen","orcid":"https://orcid.org/0009-0006-8506-6464"},"institutions":[{"id":"https://openalex.org/I4210100430","display_name":"Google (Switzerland)","ror":"https://ror.org/014f9c269","country_code":"CH","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210100430","https://openalex.org/I4210128969"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Pierre Ruyssen","raw_affiliation_strings":["Google Brain, Google Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Google Brain, Google Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I4210100430"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.888,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.805927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":82,"max":84},"biblio":{"volume":"34","issue":"1","first_page":"171","last_page":"185"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9999,"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":0.9999,"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/T10057","display_name":"Face and Expression Recognition","score":0.9994,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9993,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.7873806},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6429524}],"concepts":[{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.7873806},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6429524},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6013167},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.59827435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5831558},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.45538923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44114253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28674686},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27803564},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27466932},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24975199},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15089676},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.14833477},{"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/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3091598","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1908.00461","pdf_url":"https://arxiv.org/pdf/1908.00461","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34232894","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_indexed_in_scopus":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":["National Institutes of Health"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1908.00461","pdf_url":"https://arxiv.org/pdf/1908.00461","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320320766","funder_display_name":"Nanyang Technological University","award_id":null},{"funder":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","award_id":"172815"}],"datasets":[],"versions":[],"referenced_works_count":24,"referenced_works":["https://openalex.org/W1987083649","https://openalex.org/W1987423623","https://openalex.org/W199797433","https://openalex.org/W2057624533","https://openalex.org/W2059639989","https://openalex.org/W2075103606","https://openalex.org/W2096642693","https://openalex.org/W2097596242","https://openalex.org/W2098589050","https://openalex.org/W2124541940","https://openalex.org/W2145962650","https://openalex.org/W2149532724","https://openalex.org/W2153636395","https://openalex.org/W2167732364","https://openalex.org/W2175634846","https://openalex.org/W2190254461","https://openalex.org/W2233138502","https://openalex.org/W2271840356","https://openalex.org/W2463935670","https://openalex.org/W2503308866","https://openalex.org/W2904890392","https://openalex.org/W2912984848","https://openalex.org/W4301014524","https://openalex.org/W4302444439"],"related_works":["https://openalex.org/W4250375811","https://openalex.org/W2361081803","https://openalex.org/W2153421756","https://openalex.org/W2125213988","https://openalex.org/W2109057766","https://openalex.org/W2078644396","https://openalex.org/W2077818434","https://openalex.org/W2054489697","https://openalex.org/W2036241269","https://openalex.org/W2026930022"],"abstract_inverted_index":{"This":[0],"article":[1],"revisits":[2],"the":[3,35,41,44,48,55,59,62,87,108,111,123,133,140,143,146,151],"problem":[4],"of":[5,14,58,82,89,110,126,135,142,148,150],"decomposing":[6],"a":[7,12,15,18,22,79,90,97,119],"positive":[8],"semidefinite":[9],"matrix":[10,16,36,81],"as":[11,61],"sum":[13],"with":[17],"given":[19],"rank":[20],"plus":[21],"sparse":[23],"matrix.":[24],"An":[25],"immediate":[26],"application":[27],"can":[28],"be":[29,38],"found":[30],"in":[31,47,53,139],"portfolio":[32],"optimization,":[33],"when":[34],"to":[37,101,118],"decomposed":[39],"is":[40,78],"covariance":[42],"between":[43],"different":[45],"assets":[46],"portfolio.":[49],"Our":[50],"approach":[51],"consists":[52],"representing":[54],"low-rank":[56],"part":[57],"solution":[60],"product":[63],"":[66,74],"$MM^{T}$":[68],"":[69,77],",":[70],"where":[71],"notation=\"LaTeX\">$M$":[76],"rectangular":[80],"appropriate":[83,104],"size,":[84],"parametrized":[85],"by":[86],"coefficients":[88],"deep":[91],"neural":[92],"network.":[93,112],"We":[94,113,130],"then":[95],"use":[96],"gradient":[98],"descent":[99],"algorithm":[100],"minimize":[102],"an":[103],"loss":[105,128],"function":[106],"over":[107],"parameters":[109],"deduce":[114],"its":[115],"convergence":[116,136],"rate":[117,134],"local":[120],"optimum":[121],"from":[122],"Lipschitz":[124],"smoothness":[125],"our":[127],"function.":[129],"show":[131],"that":[132],"grows":[137],"polynomially":[138],"dimensions":[141],"input\u2013output,":[144],"and":[145],"size":[147],"each":[149],"hidden":[152],"layers.":[153]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3182435136","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-03-17T12:13:17.788851","created_date":"2021-07-19"}