{"id":"https://openalex.org/W3111358795","doi":"https://doi.org/10.1561/2200000079","title":"Spectral Methods for Data Science: A Statistical Perspective","display_name":"Spectral Methods for Data Science: A Statistical Perspective","publication_year":2021,"publication_date":"2021-10-21","ids":{"openalex":"https://openalex.org/W3111358795","doi":"https://doi.org/10.1561/2200000079","mag":"3111358795"},"language":"en","primary_location":{"id":"doi:10.1561/2200000079","is_oa":false,"landing_page_url":"https://doi.org/10.1561/2200000079","pdf_url":null,"source":{"id":"https://openalex.org/S4210188176","display_name":"Foundations and Trends\u00ae in Machine Learning","issn_l":"1935-8237","issn":["1935-8237","1935-8245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2012.08496","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yuxin Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yuxin Chen","raw_affiliation_strings":["Princeton University"],"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yuejie Chi","orcid":null},"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":"Yuejie Chi","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jianqing Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianqing Fan","raw_affiliation_strings":["Princeton University"],"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":null,"display_name":"Cong Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cong Ma","raw_affiliation_strings":["University of Chicago"],"affiliations":[{"raw_affiliation_string":"University of Chicago","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":15.6076,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.99424175,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"14","issue":"5","first_page":"566","last_page":"806"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.7070000171661377,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.7070000171661377,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.07259999960660934,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.019200000911951065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5133000016212463},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4530999958515167},{"id":"https://openalex.org/keywords/synthetic-data","display_name":"Synthetic data","score":0.37929999828338623},{"id":"https://openalex.org/keywords/missing-data","display_name":"Missing data","score":0.3765000104904175},{"id":"https://openalex.org/keywords/spectral-density-estimation","display_name":"Spectral density estimation","score":0.3749000132083893},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.35260000824928284},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.3483000099658966},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.34790000319480896},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.3467999994754791},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.3465000092983246}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5218999981880188},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5133000016212463},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4747999906539917},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4530999958515167},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4221000075340271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.398499995470047},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C30049272","wikidata":"https://www.wikidata.org/wiki/Q6555326","display_name":"Spectral density estimation","level":3,"score":0.3749000132083893},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.34709998965263367},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.3467999994754791},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3465000092983246},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.34130001068115234},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33970001339912415},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.31700000166893005},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.31619998812675476},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C43091099","wikidata":"https://www.wikidata.org/wiki/Q1067788","display_name":"Through-the-lens metering","level":3,"score":0.3010999858379364},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3003999888896942},{"id":"https://openalex.org/C2776285698","wikidata":"https://www.wikidata.org/wiki/Q2642214","display_name":"Exposition (narrative)","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.28049999475479126},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.271699994802475},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C48057537","wikidata":"https://www.wikidata.org/wiki/Q3551145","display_name":"Statistical theory","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.2700999975204468},{"id":"https://openalex.org/C120894424","wikidata":"https://www.wikidata.org/wiki/Q1322871","display_name":"Exploratory data analysis","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C133462117","wikidata":"https://www.wikidata.org/wiki/Q4929239","display_name":"Data collection","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25859999656677246},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.2522999942302704}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1561/2200000079","is_oa":false,"landing_page_url":"https://doi.org/10.1561/2200000079","pdf_url":null,"source":{"id":"https://openalex.org/S4210188176","display_name":"Foundations and Trends\u00ae in Machine Learning","issn_l":"1935-8237","issn":["1935-8237","1935-8245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2012.08496","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.08496","pdf_url":"https://arxiv.org/pdf/2012.08496","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:aleph.bib-bvb.de:BVB01-033307196","is_oa":false,"landing_page_url":"https://www.nowpublishers.com/article/Details/MAL-079","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"software, multimedia"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2012.08496","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.08496","pdf_url":"https://arxiv.org/pdf/2012.08496","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":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Spectral":[0],"methods":[1,24,105,132,189,224],"have":[2,56],"emerged":[3],"as":[4,110],"a":[5,21,27,111,181,191,227,259,279],"simple":[6],"yet":[7,184],"surprisingly":[8],"effective":[9],"approach":[10],"for":[11,266],"extracting":[12],"information":[13],"from":[14,49,190],"massive,":[15],"noisy":[16],"and":[17,38,65,68,102,142,171,233,247,262,268],"incomplete":[18],"data.":[19,50],"In":[20,203,250],"nutshell,":[22],"spectral":[23,104,131,188,223],"refer":[25],"to":[26,99,118,124,137,179,187,217,235,252,278],"collection":[28],"of":[29,43,54,130,145,162,168,222,230,242],"algorithms":[30,123],"built":[31],"upon":[32],"the":[33,128,143,147,160,166,219,240],"eigenvalues":[34],"(resp.":[35,40],"singular":[36,41,269],"values)":[37],"eigenvectors":[39],"vectors)":[42],"some":[44],"properly":[45],"designed":[46],"matrices":[47],"constructed":[48],"A":[51],"diverse":[52,200],"array":[53],"applications":[55],"been":[57],"found":[58],"in":[59,155,199,225,239],"machine":[60],"learning,":[61],"imaging":[62],"science,":[63],"financial":[64,88],"econometric":[66],"modeling,":[67,164],"signal":[69],"processing,":[70],"including":[71],"recommendation":[72],"systems,":[73],"community":[74],"detection,":[75],"ranking,":[76],"structured":[77],"matrix":[78,139,174],"recovery,":[79],"tensor":[80],"data":[81],"estimation,":[82],"joint":[83],"shape":[84],"matching,":[85],"blind":[86],"deconvolution,":[87],"investments,":[89],"risk":[90],"managements,":[91],"treatment":[92],"evaluations,":[93],"causal":[94],"inference,":[95],"amongst":[96],"others.":[97],"Due":[98],"their":[100,157,196,237],"simplicity":[101],"effectiveness,":[103],"are":[106],"not":[107],"only":[108,273],"used":[109],"stand-alone":[112],"estimator,":[113],"but":[114],"also":[115],"frequently":[116],"employed":[117],"facilitate":[119],"other":[120],"more":[121],"sophisticated":[122],"enhance":[125],"performance.":[126],"While":[127],"studies":[129],"can":[133],"be":[134],"traced":[135],"back":[136],"classical":[138],"perturbation":[140,255,264],"theory":[141,265],"method":[144],"moments,":[146],"past":[148],"decade":[149],"has":[150,272],"witnessed":[151],"tremendous":[152],"theoretical":[153],"advances":[154],"demystifying":[156],"efficacy":[158],"through":[159],"lens":[161],"statistical":[163,193,231],"with":[165],"aid":[167],"concentration":[169],"inequalities":[170],"non-asymptotic":[172],"random":[173,243],"theory.":[175],"This":[176],"monograph":[177],"aims":[178],"present":[180,258],"systematic,":[182],"comprehensive,":[183],"accessible":[185],"introduction":[186],"modern":[192],"perspective,":[194],"highlighting":[195],"algorithmic":[197],"implications":[198],"large-scale":[201],"applications.":[202],"particular,":[204],"our":[205],"exposition":[206],"gravitates":[207],"around":[208],"several":[209],"central":[210],"questions":[211],"that":[212],"span":[213],"various":[214],"applications:":[215],"how":[216,234],"characterize":[218],"sample":[220],"efficiency":[221],"reaching":[226],"target":[228],"level":[229],"accuracy,":[232],"assess":[236],"stability":[238],"face":[241],"noise,":[244],"missing":[245],"data,":[246],"adversarial":[248],"corruptions?":[249],"addition":[251],"conventional":[253],"\u21132":[254],"analysis,":[256],"we":[257],"systematic":[260],"\u2113\u221e":[261],"\u21132,\u221e":[263],"eigenspace":[267],"subspaces,":[270],"which":[271],"recently":[274],"become":[275],"available":[276],"owing":[277],"powerful":[280],"\u201cleave-one-out\u201d":[281],"analysis":[282],"framework.":[283]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":31},{"year":2024,"cited_by_count":26},{"year":2023,"cited_by_count":25},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2020-12-21T00:00:00"}