{"id":"https://openalex.org/W3201018963","doi":"https://doi.org/10.1109/tit.2021.3112821","title":"How to Reduce Dimension With PCA and Random Projections?","display_name":"How to Reduce Dimension With PCA and Random Projections?","publication_year":2021,"publication_date":"2021-09-14","ids":{"openalex":"https://openalex.org/W3201018963","doi":"https://doi.org/10.1109/tit.2021.3112821","mag":"3201018963","pmid":"https://pubmed.ncbi.nlm.nih.gov/35695837"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3112821","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3112821","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9173709","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080010066","display_name":"Fan Yang","orcid":"https://orcid.org/0000-0001-6972-0784"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fan Yang","raw_affiliation_strings":["Wharton Statistics Department, University of Pennsylvania, Philadelphia, PA 19104, USA","Wharton Statistics Department, University of Pennsylvania, Philadelphia, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wharton Statistics Department, University of Pennsylvania, Philadelphia, PA 19104, USA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"Wharton Statistics Department, University of Pennsylvania, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070605006","display_name":"Sifan Liu","orcid":"https://orcid.org/0000-0002-1608-4216"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sifan Liu","raw_affiliation_strings":["Department of Statistics, Stanford University, Stanford, CA 94305, USA","Department of Statistics, Stanford University, Stanford, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1608-4216","affiliations":[{"raw_affiliation_string":"Department of Statistics, Stanford University, Stanford, CA 94305, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Statistics, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031235093","display_name":"Edgar Dobriban","orcid":"https://orcid.org/0000-0002-3467-8931"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edgar Dobriban","raw_affiliation_strings":["Wharton Statistics Department, University of Pennsylvania, Philadelphia, PA 19104, USA","Wharton Statistics Department, University of Pennsylvania, Philadelphia, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-3467-8931","affiliations":[{"raw_affiliation_string":"Wharton Statistics Department, University of Pennsylvania, Philadelphia, PA 19104, USA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"Wharton Statistics Department, University of Pennsylvania, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102861589","display_name":"David P. Woodruff","orcid":"https://orcid.org/0000-0002-2158-1380"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David P. Woodruff","raw_affiliation_strings":["Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA","Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3869,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.93002851,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"67","issue":"12","first_page":"8154","last_page":"8189"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9986000061035156,"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/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/random-projection","display_name":"Random projection","score":0.7349067330360413},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.7277394533157349},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.6333267688751221},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.516832172870636},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.48557087779045105},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.47607678174972534},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4722268581390381},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.4717603325843811},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46664953231811523},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4621155560016632},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4584465026855469},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.41620075702667236},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3979879915714264},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3887854814529419},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.33088070154190063},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2580052614212036}],"concepts":[{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.7349067330360413},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.7277394533157349},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.6333267688751221},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.516832172870636},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.48557087779045105},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.47607678174972534},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4722268581390381},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.4717603325843811},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46664953231811523},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4621155560016632},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4584465026855469},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.41620075702667236},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3979879915714264},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3887854814529419},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.33088070154190063},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2580052614212036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2021.3112821","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3112821","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmid:35695837","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35695837","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 information theory","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:9173709","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9173709","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Trans Inf Theory","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:9173709","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9173709","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Trans Inf Theory","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1179829695","display_name":null,"funder_award_id":"N00014-18-1-256","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4841703938","display_name":null,"funder_award_id":"5R01 HG 10798-2","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G8327040736","display_name":null,"funder_award_id":"IIS 1837992","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G981263030","display_name":null,"funder_award_id":"1934960","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":152,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W93530381","https://openalex.org/W143531921","https://openalex.org/W615589970","https://openalex.org/W1493892051","https://openalex.org/W1505090736","https://openalex.org/W1520752838","https://openalex.org/W1556219185","https://openalex.org/W1576778649","https://openalex.org/W1577871831","https://openalex.org/W1586554030","https://openalex.org/W1783487834","https://openalex.org/W1945899805","https://openalex.org/W1968691112","https://openalex.org/W1979541448","https://openalex.org/W1979750072","https://openalex.org/W1995241424","https://openalex.org/W1999352252","https://openalex.org/W2003571173","https://openalex.org/W2007399394","https://openalex.org/W2011892826","https://openalex.org/W2012713405","https://openalex.org/W2017304912","https://openalex.org/W2020027197","https://openalex.org/W2027777023","https://openalex.org/W2034680120","https://openalex.org/W2037037201","https://openalex.org/W2038801368","https://openalex.org/W2040387238","https://openalex.org/W2043804332","https://openalex.org/W2044172468","https://openalex.org/W2045390367","https://openalex.org/W2060581589","https://openalex.org/W2063698478","https://openalex.org/W2066459155","https://openalex.org/W2076549096","https://openalex.org/W2085739863","https://openalex.org/W2086323639","https://openalex.org/W2089817321","https://openalex.org/W2097576041","https://openalex.org/W2099551908","https://openalex.org/W2102714321","https://openalex.org/W2105234758","https://openalex.org/W2106084579","https://openalex.org/W2107411554","https://openalex.org/W2116780995","https://openalex.org/W2117756735","https://openalex.org/W2117920736","https://openalex.org/W2121689290","https://openalex.org/W2131172946","https://openalex.org/W2132657058","https://openalex.org/W2133487567","https://openalex.org/W2135921993","https://openalex.org/W2138136390","https://openalex.org/W2143364091","https://openalex.org/W2144497295","https://openalex.org/W2152356156","https://openalex.org/W2152402969","https://openalex.org/W2157988812","https://openalex.org/W2177697562","https://openalex.org/W2187483593","https://openalex.org/W2220487585","https://openalex.org/W2256075469","https://openalex.org/W2283127439","https://openalex.org/W2284253967","https://openalex.org/W2342249230","https://openalex.org/W2404067730","https://openalex.org/W2488424576","https://openalex.org/W2580753685","https://openalex.org/W2590556189","https://openalex.org/W2593245224","https://openalex.org/W2615055317","https://openalex.org/W2772646190","https://openalex.org/W2799499928","https://openalex.org/W2884552970","https://openalex.org/W2890952928","https://openalex.org/W2896224263","https://openalex.org/W2900374875","https://openalex.org/W2952676558","https://openalex.org/W2954942261","https://openalex.org/W2962723202","https://openalex.org/W2962735967","https://openalex.org/W2962842430","https://openalex.org/W2962946304","https://openalex.org/W2963002486","https://openalex.org/W2963060476","https://openalex.org/W2963459305","https://openalex.org/W2963649004","https://openalex.org/W2963773113","https://openalex.org/W2963780177","https://openalex.org/W2963975913","https://openalex.org/W2964044082","https://openalex.org/W2965497096","https://openalex.org/W2970072822","https://openalex.org/W2978131577","https://openalex.org/W2978296194","https://openalex.org/W2997636101","https://openalex.org/W3004236690","https://openalex.org/W3046808689","https://openalex.org/W3087034383","https://openalex.org/W3098031198","https://openalex.org/W3098045837","https://openalex.org/W3098324794","https://openalex.org/W3098650594","https://openalex.org/W3099053901","https://openalex.org/W3099134300","https://openalex.org/W3100283647","https://openalex.org/W3100639561","https://openalex.org/W3101588691","https://openalex.org/W3101939483","https://openalex.org/W3102939586","https://openalex.org/W3103096700","https://openalex.org/W3103692684","https://openalex.org/W3105263018","https://openalex.org/W3106436031","https://openalex.org/W3112410551","https://openalex.org/W3122283149","https://openalex.org/W3122991289","https://openalex.org/W3127939736","https://openalex.org/W3139361274","https://openalex.org/W3150749950","https://openalex.org/W3152110893","https://openalex.org/W3166788073","https://openalex.org/W4213099427","https://openalex.org/W4213311204","https://openalex.org/W4249843299","https://openalex.org/W4250857377","https://openalex.org/W4256144076","https://openalex.org/W4289259534","https://openalex.org/W4293471561","https://openalex.org/W4297776040","https://openalex.org/W4297817021","https://openalex.org/W4399522907","https://openalex.org/W6603787252","https://openalex.org/W6631139464","https://openalex.org/W6634440824","https://openalex.org/W6650267568","https://openalex.org/W6677280552","https://openalex.org/W6679168169","https://openalex.org/W6679963453","https://openalex.org/W6682597329","https://openalex.org/W6683016151","https://openalex.org/W6685688796","https://openalex.org/W6686785280","https://openalex.org/W6713434571","https://openalex.org/W6734065873","https://openalex.org/W6747251814","https://openalex.org/W6755333959","https://openalex.org/W6767082502","https://openalex.org/W6768633674","https://openalex.org/W6785248507","https://openalex.org/W6910505072"],"related_works":["https://openalex.org/W2611813480","https://openalex.org/W2141406155","https://openalex.org/W2089497633","https://openalex.org/W3015962327","https://openalex.org/W1484758315","https://openalex.org/W2105715935","https://openalex.org/W1974715691","https://openalex.org/W2370292837","https://openalex.org/W1980171335","https://openalex.org/W1965604469"],"abstract_inverted_index":{"In":[0,62],"our":[1,126],"\"big":[2],"data\"":[3],"age,":[4],"the":[5,73,97,137,144,147,177,180,183,229],"size":[6],"and":[7,22,37,39,58,80,91,133,182,222,236],"complexity":[8],"of":[9,27,75,99,179,203],"data":[10,120,181,223],"is":[11,150],"steadily":[12],"increasing.":[13],"Methods":[14],"for":[15,55,60,219],"dimension":[16,28,149],"reduction":[17,29],"are":[18,30,140,189,231],"ever":[19],"more":[20,158,191],"popular":[21,101],"useful.":[23],"Two":[24],"distinct":[25],"types":[26],"\"data-oblivious\"":[31],"methods":[32,41,82,103],"such":[33,42,52],"as":[34,43,53],"random":[35,56,86,107],"projections":[36,188],"sketching,":[38],"\"data-aware\"":[40],"principal":[44],"component":[45],"analysis":[46],"(PCA).":[47],"Both":[48],"have":[49,217],"their":[50],"strengths,":[51],"speed":[54],"projections,":[57,106],"data-adaptivity":[59],"PCA.":[61],"this":[63],"work,":[64],"we":[65],"study":[66,78,154],"how":[67],"to":[68,71,123,201],"combine":[69],"them":[70],"get":[72],"best":[74],"both.":[76],"We":[77,95,152,162,225],"\"sketch":[79],"solve\"":[81],"that":[83,164,228],"take":[84],"a":[85,115,172,212],"projection":[87,148,170],"(or":[88,118],"sketch)":[89],"first,":[90],"compute":[92,96],"PCA":[93],"after.":[94],"performance":[98],"several":[100],"sketching":[102,184],"(random":[104],"iid":[105],"sampling,":[108],"subsampled":[109],"Hadamard":[110],"transform,":[111],"CountSketch,":[112],"etc)":[113],"in":[114,171,234,237],"general":[116,159],"\"signal-plus-noise\"":[117],"spiked)":[119],"model.":[121],"Compared":[122],"well-known":[124],"works,":[125],"results":[127,216,230],"(1)":[128],"give":[129],"asymptotically":[130],"exact":[131],"results,":[132],"(2)":[134],"apply":[135],"when":[136],"signal":[138,166],"components":[139],"only":[141],"slightly":[142,190],"above":[143],"noise,":[145],"but":[146],"non-negligible.":[151],"also":[153,226],"stronger":[155],"signals":[156],"allowing":[157],"covariance":[160],"structures.":[161],"find":[163],"(a)":[165],"strength":[167],"decreases":[168],"under":[169],"delicate":[173],"way":[174],"depending":[175],"on":[176],"structure":[178],"method,":[185],"(b)":[186],"orthogonal":[187],"accurate,":[192],"(c)":[193],"randomization":[194],"does":[195],"not":[196],"hurt":[197],"too":[198],"much,":[199],"due":[200],"concentration":[202],"measure,":[204],"(d)":[205],"CountSketch":[206],"can":[207],"be":[208],"somewhat":[209],"improved":[210],"by":[211],"normalization":[213],"method.":[214],"Our":[215],"implications":[218],"statistical":[220],"learning":[221],"analysis.":[224],"illustrate":[227],"highly":[232],"accurate":[233],"simulations":[235],"analyzing":[238],"empirical":[239],"data.":[240]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
