{"id":"https://openalex.org/W2744864415","doi":"https://doi.org/10.1109/isit.2017.8007083","title":"Spectral initialization for nonconvex estimation: High-dimensional limit and phase transitions","display_name":"Spectral initialization for nonconvex estimation: High-dimensional limit and phase transitions","publication_year":2017,"publication_date":"2017-06-01","ids":{"openalex":"https://openalex.org/W2744864415","doi":"https://doi.org/10.1109/isit.2017.8007083","mag":"2744864415"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2017.8007083","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2017.8007083","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE International Symposium on Information Theory (ISIT)","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/A5038111389","display_name":"Yue M. Lu","orcid":"https://orcid.org/0000-0002-5174-2595"},"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":"Yue M. Lu","raw_affiliation_strings":["Paulson School of Engineering and Applied Sciences, Harvard University, USA"],"affiliations":[{"raw_affiliation_string":"Paulson School of Engineering and Applied Sciences, Harvard University, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100357060","display_name":"Gen Li","orcid":"https://orcid.org/0009-0005-9782-7649"},"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":"Gen Li","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua University, China"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038111389"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":4.3218,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.9485561,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"3015","last_page":"3019"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"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":0.9991000294685364,"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/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/hypersphere","display_name":"Hypersphere","score":0.8050272464752197},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.6970019936561584},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6332756280899048},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5350134968757629},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5148764848709106},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4796321988105774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.466778427362442},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.45613744854927063},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41340476274490356},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3311934769153595},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17126628756523132},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1445103883743286},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12919962406158447}],"concepts":[{"id":"https://openalex.org/C2776562905","wikidata":"https://www.wikidata.org/wiki/Q306610","display_name":"Hypersphere","level":2,"score":0.8050272464752197},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6970019936561584},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6332756280899048},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5350134968757629},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5148764848709106},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4796321988105774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.466778427362442},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.45613744854927063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41340476274490356},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3311934769153595},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17126628756523132},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1445103883743286},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12919962406158447},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2017.8007083","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2017.8007083","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1520752838","https://openalex.org/W1901790663","https://openalex.org/W2002182974","https://openalex.org/W2007593159","https://openalex.org/W2078397124","https://openalex.org/W2115645605","https://openalex.org/W2120058354","https://openalex.org/W2142949395","https://openalex.org/W2145080587","https://openalex.org/W2163353827","https://openalex.org/W2169501582","https://openalex.org/W2338490279","https://openalex.org/W2399198888","https://openalex.org/W2462226338","https://openalex.org/W2542482481","https://openalex.org/W2744864415","https://openalex.org/W2963443408","https://openalex.org/W2964262188","https://openalex.org/W3102206315","https://openalex.org/W4298263336","https://openalex.org/W6683110664","https://openalex.org/W6712627111"],"related_works":["https://openalex.org/W2099702253","https://openalex.org/W2059484267","https://openalex.org/W1970780628","https://openalex.org/W2069017679","https://openalex.org/W2133653616","https://openalex.org/W2921850681","https://openalex.org/W2079494444","https://openalex.org/W4389755575","https://openalex.org/W2466608391","https://openalex.org/W2100282197"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,9,13,71,86],"simple":[3],"spectral":[4,62,94],"method":[5,63,95],"that":[6,75],"serves":[7],"as":[8],"key":[10],"ingredient":[11],"in":[12,25,64],"growing":[14],"line":[15],"of":[16,57,60],"work":[17],"using":[18],"efficient":[19],"iterative":[20],"algorithms":[21],"for":[22],"estimating":[23],"signals":[24],"nonconvex":[26],"settings.":[27],"Unlike":[28],"previous":[29],"work,":[30],"which":[31],"focuses":[32],"on":[33,42,77],"the":[34,43,58,61,65,78,82,89,93,105,108,111,117,131],"phase":[35,72],"retrieval":[36],"setting":[37],"and":[38,52,122,129],"provides":[39],"only":[40],"bounds":[41],"performance,":[44],"we":[45],"consider":[46],"arbitrary":[47],"generalized":[48],"linear":[49],"sensing":[50],"models":[51],"provide":[53],"an":[54],"exact":[55],"characterization":[56],"performance":[59],"high-dimensional":[66],"regime.":[67],"Our":[68],"analysis":[69],"reveals":[70],"transition":[73],"phenomenon":[74],"depends":[76],"sampling":[79],"ratio.":[80],"When":[81],"ratio":[83],"is":[84],"below":[85],"critical":[87],"threshold,":[88,109],"estimates":[90,112],"given":[91],"by":[92],"are":[96,125],"no":[97],"better":[98],"than":[99],"random":[100],"guesses":[101],"drawn":[102],"uniformly":[103],"from":[104],"hypersphere;":[106],"above":[107],"however,":[110],"become":[113],"increasingly":[114],"aligned":[115],"with":[116],"underlying":[118],"signal.":[119],"Worked":[120],"examples":[121],"numerical":[123],"simulations":[124],"provided":[126],"to":[127],"illustrate":[128],"verify":[130],"analytical":[132],"predictions.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}