{"id":"https://openalex.org/W2981615287","doi":"https://doi.org/10.1137/20m1379745","title":"Deterministic Tensor Completion with Hypergraph Expanders","display_name":"Deterministic Tensor Completion with Hypergraph Expanders","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2981615287","doi":"https://doi.org/10.1137/20m1379745","mag":"2981615287"},"language":"en","primary_location":{"id":"doi:10.1137/20m1379745","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1379745","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/20m1379745","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060223489","display_name":"Kameron Decker Harris","orcid":"https://orcid.org/0000-0002-3716-6173"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kameron Decker Harris","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3716-6173","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028927697","display_name":"Yizhe Zhu","orcid":"https://orcid.org/0000-0002-5665-0374"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yizhe Zhu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5665-0374","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060223489"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.138,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.29196217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":"4","first_page":"1117","last_page":"1140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9747999906539917,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/hypergraph","display_name":"Hypergraph","score":0.7949837446212769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6918308734893799},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6700210571289062},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5239629745483398},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5068727135658264},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.48587459325790405},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.411730021238327},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41160207986831665},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25150442123413086}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7949837446212769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6918308734893799},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6700210571289062},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5239629745483398},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5068727135658264},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.48587459325790405},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.411730021238327},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41160207986831665},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25150442123413086},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1379745","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1379745","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1910.10692","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.10692","pdf_url":"https://arxiv.org/pdf/1910.10692","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":"mag:2981615287","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1910.10692","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1910.10692","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1910.10692","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1137/20m1379745","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1379745","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3790747580","display_name":null,"funder_award_id":"DMS-1949617","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/F4320306854","display_name":"Washington Research Foundation","ror":"https://ror.org/00hasdx88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":72,"referenced_works":["https://openalex.org/W130436789","https://openalex.org/W1492459858","https://openalex.org/W1521672915","https://openalex.org/W1539416424","https://openalex.org/W1545868355","https://openalex.org/W1577058896","https://openalex.org/W1578099820","https://openalex.org/W1631603072","https://openalex.org/W1871180460","https://openalex.org/W1885765327","https://openalex.org/W1970776428","https://openalex.org/W1976618413","https://openalex.org/W1979110822","https://openalex.org/W2006822886","https://openalex.org/W2015393836","https://openalex.org/W2018047324","https://openalex.org/W2024165284","https://openalex.org/W2047342855","https://openalex.org/W2051569409","https://openalex.org/W2055656009","https://openalex.org/W2060493211","https://openalex.org/W2061924414","https://openalex.org/W2069652865","https://openalex.org/W2076342873","https://openalex.org/W2078677240","https://openalex.org/W2079705627","https://openalex.org/W2091449379","https://openalex.org/W2095087473","https://openalex.org/W2095534914","https://openalex.org/W2108138101","https://openalex.org/W2120872934","https://openalex.org/W2127491574","https://openalex.org/W2129700748","https://openalex.org/W2130270608","https://openalex.org/W2130800351","https://openalex.org/W2134490689","https://openalex.org/W2144730813","https://openalex.org/W2579795020","https://openalex.org/W2593198395","https://openalex.org/W2746420172","https://openalex.org/W2749418260","https://openalex.org/W2799186957","https://openalex.org/W2951839680","https://openalex.org/W2962804816","https://openalex.org/W2963310150","https://openalex.org/W2963472624","https://openalex.org/W2963553724","https://openalex.org/W2963677571","https://openalex.org/W2963725088","https://openalex.org/W2963861568","https://openalex.org/W2963931849","https://openalex.org/W2964021737","https://openalex.org/W2964024102","https://openalex.org/W2964075618","https://openalex.org/W2964115409","https://openalex.org/W2964121447","https://openalex.org/W2972821414","https://openalex.org/W2977217991","https://openalex.org/W2990423062","https://openalex.org/W3031055522","https://openalex.org/W3034260800","https://openalex.org/W3035192619","https://openalex.org/W3038279281","https://openalex.org/W3080832086","https://openalex.org/W3098807808","https://openalex.org/W3099823322","https://openalex.org/W3100295572","https://openalex.org/W3106800436","https://openalex.org/W3109157652","https://openalex.org/W3159451596","https://openalex.org/W3163742575","https://openalex.org/W3191387004"],"related_works":["https://openalex.org/W2143160814","https://openalex.org/W2990073718","https://openalex.org/W3104844238","https://openalex.org/W3198145171","https://openalex.org/W2010106582","https://openalex.org/W2028932986","https://openalex.org/W3109156225","https://openalex.org/W2964165785","https://openalex.org/W3046735073","https://openalex.org/W2810899983","https://openalex.org/W3010060024","https://openalex.org/W2997404769","https://openalex.org/W3021044972","https://openalex.org/W3170397223","https://openalex.org/W2569499781","https://openalex.org/W2158624781","https://openalex.org/W3105442588","https://openalex.org/W1815722773","https://openalex.org/W1761820742","https://openalex.org/W3081646966"],"abstract_inverted_index":{"We":[0,115],"provide":[1],"a":[2,14,80,86,117,122],"novel":[3],"analysis":[4,32,111],"of":[5,22,40,68,103,112,125],"low-rank":[6],"tensor":[7,48,70,98,113],"completion":[8],"based":[9],"on":[10],"hypergraph":[11,90],"expanders.":[12],"As":[13,73],"proxy":[15],"for":[16,29,85],"rank,":[17],"we":[18,78,131],"minimize":[19],"the":[20,23,27,38,61,64,69,101,108,126],"max-quasinorm":[21,127],"tensor,":[24],"which":[25],"generalizes":[26],"max-norm":[28],"matrices.":[30],"Our":[31],"is":[33,56,107],"deterministic":[34,110],"and":[35,66,92,130],"shows":[36],"that":[37,63,120],"number":[39],"samples":[41],"required":[42],"to":[43],"approximately":[44],"recover":[45],"an":[46],"order-$t$":[47],"with":[49,135],"at":[50],"most":[51],"$n$":[52],"entries":[53],"per":[54],"dimension":[55],"linear":[57],"in":[58,75],"$n$,":[59],"under":[60],"assumption":[62],"rank":[65],"order":[67],"are":[71],"$O(1)$.":[72],"steps":[74],"our":[76,104],"proof,":[77],"find":[79],"new":[81,95],"expander":[82],"mixing":[83],"lemma":[84],"$t$-partite,":[87],"$t$-uniform":[88],"regular":[89],"model,":[91],"prove":[93],"several":[94],"properties":[96],"about":[97],"max-quasinorm.":[99],"To":[100],"best":[102],"knowledge,":[105],"this":[106],"first":[109],"completion.":[114],"develop":[116],"practical":[118],"algorithm":[119],"solves":[121],"relaxed":[123],"version":[124],"minimization":[128],"problem,":[129],"demonstrate":[132],"its":[133],"efficacy":[134],"numerical":[136],"experiments.":[137]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}