{"id":"https://openalex.org/W3081103457","doi":"https://doi.org/10.1109/isit44484.2020.9174072","title":"On the Sample Complexity of Estimating Small Singular Modes","display_name":"On the Sample Complexity of Estimating Small Singular Modes","publication_year":2020,"publication_date":"2020-06-01","ids":{"openalex":"https://openalex.org/W3081103457","doi":"https://doi.org/10.1109/isit44484.2020.9174072","mag":"3081103457"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit44484.2020.9174072","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-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/A5054043281","display_name":"Xiangxiang Xu","orcid":"https://orcid.org/0000-0002-4178-0934"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangxiang Xu","raw_affiliation_strings":["Dept. of Electronic Engineering, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Dept. of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101800202","display_name":"Weida Wang","orcid":"https://orcid.org/0009-0007-7241-7701"},"institutions":[{"id":"https://openalex.org/I4210114105","display_name":"Tsinghua\u2013Berkeley Shenzhen Institute","ror":"https://ror.org/02hhwwz98","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114105","https://openalex.org/I95457486","https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weida Wang","raw_affiliation_strings":["DSIT Research Center, Tsinghua-Berkeley Shenzhen Institute, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"DSIT Research Center, Tsinghua-Berkeley Shenzhen Institute, Shenzhen, China","institution_ids":["https://openalex.org/I4210114105"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102003146","display_name":"Shao-Lun Huang","orcid":"https://orcid.org/0000-0001-7020-5456"},"institutions":[{"id":"https://openalex.org/I4210114105","display_name":"Tsinghua\u2013Berkeley Shenzhen Institute","ror":"https://ror.org/02hhwwz98","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114105","https://openalex.org/I95457486","https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shao-Lun Huang","raw_affiliation_strings":["DSIT Research Center, Tsinghua-Berkeley Shenzhen Institute, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"DSIT Research Center, Tsinghua-Berkeley Shenzhen Institute, Shenzhen, China","institution_ids":["https://openalex.org/I4210114105"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.17,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.416579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":60,"max":69},"biblio":{"volume":null,"issue":null,"first_page":"1189","last_page":"1194"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9997,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9996,"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/singular-value","display_name":"Singular value","score":0.8302002},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.63467026},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.57242846},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5492265},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.47909454}],"concepts":[{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.8302002},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.63467026},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.59525335},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.57242846},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5492265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.54308975},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5063132},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.50289243},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.5004058},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.47909454},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.44716465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38186792},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33830148},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22990394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22946507},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13494638},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.106775045},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.100293756},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit44484.2020.9174072","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":12,"referenced_works":["https://openalex.org/W1995228946","https://openalex.org/W2014311222","https://openalex.org/W2018582985","https://openalex.org/W2107327484","https://openalex.org/W2113157322","https://openalex.org/W2125031621","https://openalex.org/W2133157266","https://openalex.org/W2548842562","https://openalex.org/W2963767133","https://openalex.org/W2991489140","https://openalex.org/W3006229350","https://openalex.org/W3081103457"],"related_works":["https://openalex.org/W4386721910","https://openalex.org/W4382583540","https://openalex.org/W4378770618","https://openalex.org/W4319586039","https://openalex.org/W4094001","https://openalex.org/W2163255469","https://openalex.org/W2148568324","https://openalex.org/W2010100052","https://openalex.org/W1990844505","https://openalex.org/W1607100495"],"abstract_inverted_index":{"While":[0],"it":[1,91],"is":[2,23],"commonly":[3],"believed":[4],"that":[5,83,141],"estimating":[6,43,49,72],"the":[7,19,36,39,62,68,88,106,110,114,127,147],"small":[8,51,73,118],"singular":[9,52,74,107,111],"modes":[10,75,108],"for":[11,142],"a":[12,44,57],"nearly":[13],"low-rank":[14,148],"matrix":[15,45,63],"requires":[16,92],"more":[17],"samples,":[18,145],"sample":[20,32,89],"size":[21],"needed":[22],"generally":[24],"unclear.":[25],"In":[26,79],"this":[27,31],"paper,":[28],"we":[29,55,81,139],"investigate":[30],"complexity":[33],"by":[34,76],"considering":[35],"difference":[37],"between":[38],"estimation":[40,130],"errors":[41],"of":[42,71,116],"with":[46,109],"or":[47],"without":[48],"these":[50,151],"modes.":[53],"Specifically,":[54],"develop":[56],"mathematical":[58],"framework":[59],"based":[60],"on":[61,87],"perturbation":[64],"analysis":[65],"to":[66,103,126,160],"characterize":[67,140],"noise":[69],"level":[70],"n":[77,95],"samples.":[78],"particular,":[80],"show":[82],"under":[84],"mild":[85],"assumptions":[86],"noise,":[90],"at":[93],"least":[94],"=":[96],"O(\u03b7":[97],"-2":[100],")":[101],"samples":[102],"well":[104],"estimate":[105],"value":[112],"in":[113,150],"order":[115],"some":[117],"\u03b7.":[119],"More":[120],"importantly,":[121],"our":[122,162],"results":[123],"are":[124,153,158],"applied":[125],"channel":[128],"state":[129],"and":[131],"Hirschfeld-Gebelein-R\u00e9nyi":[132],"(HGR)":[133],"maximal":[134],"correlation":[135],"problems,":[136],"from":[137],"which":[138],"how":[143],"many":[144],"utilizing":[146],"approximation":[149],"problems":[152],"beneficial.":[154],"Finally,":[155],"numerical":[156],"simulations":[157],"provided":[159],"verify":[161],"results.":[163]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3081103457","counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2024-12-25T22:20:27.300069","created_date":"2020-09-01"}