{"id":"https://openalex.org/W2143398430","doi":"https://doi.org/10.1109/icassp.2011.5947175","title":"Estimating principal components of large covariance matrices using the Nyström method","display_name":"Estimating principal components of large covariance matrices using the Nyström method","publication_year":2011,"publication_date":"2011-05-01","ids":{"openalex":"https://openalex.org/W2143398430","doi":"https://doi.org/10.1109/icassp.2011.5947175","mag":"2143398430"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2011.5947175","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2011.5947175","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},"type":"article","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/A5085288376","display_name":"Nicholas Arcolano","orcid":null},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nicholas Arcolano","raw_affiliation_strings":["Statistics and Information Sciences Laboratory, Harvard University, Cambridge, MA, USA","Statistics and Information Sciences Laboratory, Harvard University, 33 Oxford Street, Cambridge, MA 02138, USA"],"affiliations":[{"raw_affiliation_string":"Statistics and Information Sciences Laboratory, Harvard University, Cambridge, MA, USA","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"Statistics and Information Sciences Laboratory, Harvard University, 33 Oxford Street, Cambridge, MA 02138, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065795662","display_name":"Patrick J. Wolfe","orcid":"https://orcid.org/0000-0003-3669-2777"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick J. Wolfe","raw_affiliation_strings":["Statistics and Information Sciences Laboratory, Harvard University, Cambridge, MA, USA","Statistics and Information Sciences Laboratory, Harvard University, 33 Oxford Street, Cambridge, MA 02138, USA"],"affiliations":[{"raw_affiliation_string":"Statistics and Information Sciences Laboratory, Harvard University, Cambridge, MA, USA","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"Statistics and Information Sciences Laboratory, Harvard University, 33 Oxford Street, Cambridge, MA 02138, USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085288376"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":1.7226,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.84667184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"3784","last_page":"3787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9995999932289124,"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/T11716","display_name":"Random Matrices and Applications","score":0.9983000159263611,"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/estimator","display_name":"Estimator","score":0.7473522424697876},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7108120322227478},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.6085406541824341},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6055707931518555},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.5928187370300293},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5633214116096497},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5500107407569885},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5384706258773804},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5164211392402649},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.44894054532051086},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.43581873178482056},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43543678522109985},{"id":"https://openalex.org/keywords/signal-subspace","display_name":"Signal subspace","score":0.42942190170288086},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.428445428609848},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30028611421585083},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2851110100746155},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15377363562583923},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.1280132532119751},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10216975212097168},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07963147759437561}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7473522424697876},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7108120322227478},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6085406541824341},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6055707931518555},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.5928187370300293},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5633214116096497},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5500107407569885},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5384706258773804},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5164211392402649},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.44894054532051086},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.43581873178482056},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43543678522109985},{"id":"https://openalex.org/C2777121530","wikidata":"https://www.wikidata.org/wiki/Q7512739","display_name":"Signal subspace","level":4,"score":0.42942190170288086},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.428445428609848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30028611421585083},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2851110100746155},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15377363562583923},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.1280132532119751},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10216975212097168},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07963147759437561},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2011.5947175","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2011.5947175","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","display_name":"No poverty","score":0.6700000166893005}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1520752838","https://openalex.org/W2060581589","https://openalex.org/W2062125287","https://openalex.org/W2096779346","https://openalex.org/W2112545207","https://openalex.org/W2116810533","https://openalex.org/W2119334829","https://openalex.org/W2124757684","https://openalex.org/W2142638745","https://openalex.org/W2798707604","https://openalex.org/W3105846425","https://openalex.org/W3124227816","https://openalex.org/W3148198191","https://openalex.org/W3195084822","https://openalex.org/W4255333822","https://openalex.org/W6800094421"],"related_works":["https://openalex.org/W2153912708","https://openalex.org/W2379264914","https://openalex.org/W2118094278","https://openalex.org/W2639400695","https://openalex.org/W2949173582","https://openalex.org/W4300048032","https://openalex.org/W2367577754","https://openalex.org/W2089410207","https://openalex.org/W2156673141","https://openalex.org/W2138981061"],"abstract_inverted_index":{"Covariance":[0],"matrix":[1],"estimates":[2],"are":[3,13,47],"an":[4],"essential":[5],"part":[6],"of":[7,40,53,98,109,113],"many":[8],"signal":[9],"processing":[10],"algorithms,":[11],"and":[12,36,45],"often":[14],"used":[15],"to":[16,49,92],"determine":[17],"a":[18,63,88,94,99,106],"low-dimensional":[19],"principal":[20],"subspace":[21],"via":[22],"their":[23,54],"spectral":[24],"decomposition.":[25],"However,":[26],"for":[27],"sufficiently":[28],"high-dimensional":[29],"matrices":[30],"exact":[31],"eigen-analysis":[32],"is":[33,67,80],"computationally":[34,68],"intractable,":[35],"in":[37],"the":[38,75,83,110],"case":[39],"limited":[41],"data,":[42],"sample":[43,76],"eigenvalues":[44],"eigenvectors":[46],"known":[48],"be":[50],"poor":[51],"estimators":[52],"true":[55],"counterparts.":[56],"To":[57],"address":[58],"these":[59],"issues,":[60],"we":[61],"propose":[62],"covariance":[64],"estimator":[65,115],"that":[66],"efficient":[69],"while":[70],"also":[71],"performing":[72],"shrinkage":[73],"on":[74,82],"eigenvalues.":[77],"Our":[78],"approach":[79],"based":[81],"Nystr\u00f6m":[84],"method,":[85],"which":[86],"uses":[87],"data-dependent":[89],"orthogonal":[90],"projection":[91],"obtain":[93],"fast":[95],"low-rank":[96],"approximation":[97],"large":[100],"positive":[101],"semidefinite":[102],"matrix.":[103],"We":[104],"provide":[105],"theoretical":[107],"analysis":[108],"error":[111],"properties":[112],"our":[114],"as":[116,118],"well":[117],"empirical":[119],"results.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}