{"id":"https://openalex.org/W2963774180","doi":"https://doi.org/10.1109/sampta.2015.7148922","title":"Complete dictionary recovery over the sphere","display_name":"Complete dictionary recovery over the sphere","publication_year":2015,"publication_date":"2015-05-01","ids":{"openalex":"https://openalex.org/W2963774180","doi":"https://doi.org/10.1109/sampta.2015.7148922","mag":"2963774180"},"language":"en","primary_location":{"id":"doi:10.1109/sampta.2015.7148922","doi":"https://doi.org/10.1109/sampta.2015.7148922","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sampta.2015.7148922","pdf_url":null,"source":{"id":"https://openalex.org/S4306419801","display_name":"International Conference on Sampling Theory and Applications","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 International Conference on Sampling Theory and Applications (SampTA)","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1504.06785","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011253128","display_name":"Ju Sun","orcid":"https://orcid.org/0000-0002-2017-5903","observed_orcids":["https://orcid.org/0000-0002-2017-5903"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ju Sun","raw_affiliation_strings":["Department of Electrical Engineering, Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019924950","display_name":"Qing Qu","orcid":"https://orcid.org/0000-0001-5616-7393","observed_orcids":["https://orcid.org/0000-0001-5616-7393"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qing Qu","raw_affiliation_strings":["Department of Electrical Engineering, Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019610791","display_name":"John N. Wright","orcid":"https://orcid.org/0000-0003-2683-4428","observed_orcids":["https://orcid.org/0000-0003-2683-4428"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Wright","raw_affiliation_strings":["Department of Electrical Engineering, Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":27.9749,"has_fulltext":true,"cited_by_count":72,"citation_normalized_percentile":{"value":0.99746598,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"407","last_page":"410"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":9.999999747378752e-05,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dictionary-learning","display_name":"dictionary learning","score":0.9229999780654907},{"id":"https://openalex.org/keywords/spherical-constraint","display_name":"spherical constraint","score":0.5910000205039978},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.9599999785423279},{"id":"https://openalex.org/keywords/manifold-optimization","display_name":"manifold optimization","score":0.996999979019165},{"id":"https://openalex.org/keywords/spurious-local-minima","display_name":"spurious local minima","score":0.9300000071525574},{"id":"https://openalex.org/keywords/sparse-matrix-factorization","display_name":"sparse matrix factorization","score":0.4480000138282776},{"id":"https://openalex.org/keywords/matrix-factorization","display_name":"matrix factorization","score":0.6499999761581421},{"id":"https://openalex.org/keywords/representation-learning","display_name":"representation learning","score":0.7720000147819519},{"id":"https://openalex.org/keywords/efficient-algorithms","display_name":"efficient algorithms","score":0.34200000762939453}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5038246512413025},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4186256527900696},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4102988839149475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3403233289718628},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2677112817764282}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/sampta.2015.7148922","doi":"https://doi.org/10.1109/sampta.2015.7148922","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sampta.2015.7148922","pdf_url":null,"source":{"id":"https://openalex.org/S4306419801","display_name":"International Conference on Sampling Theory and Applications","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 International Conference on Sampling Theory and Applications (SampTA)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1504.06785","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.06785","pdf_url":"https://arxiv.org/pdf/1504.06785","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.1504.06785","doi":"https://doi.org/10.48550/arxiv.1504.06785","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1504.06785","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1504.06785","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.06785","pdf_url":"https://arxiv.org/pdf/1504.06785","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6203326535","display_name":null,"funder_award_id":"N00014-13-1-0492","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7276877408","display_name":null,"funder_award_id":"ONR N00014-13-1-0492","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G984441903","display_name":"EARS: GOALI: Low-Power, Multi-Tiered, Shared-Spectrum Access Terminals using Compressive Scanning and On-Top-of-CMOS BAW Filter Banks","funder_award_id":"1343282","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/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963774180.pdf","grobid_xml":"https://content.openalex.org/works/W2963774180.grobid-xml"},"referenced_works_count":104,"referenced_works":["https://openalex.org/W10765648","https://openalex.org/W98990758","https://openalex.org/W143004564","https://openalex.org/W147998453","https://openalex.org/W180017794","https://openalex.org/W301343586","https://openalex.org/W568673721","https://openalex.org/W658559791","https://openalex.org/W1483062147","https://openalex.org/W1483804921","https://openalex.org/W1496253510","https://openalex.org/W1548802052","https://openalex.org/W1567700673","https://openalex.org/W1568896959","https://openalex.org/W1582706191","https://openalex.org/W1600586145","https://openalex.org/W1607512067","https://openalex.org/W1616556810","https://openalex.org/W1622107711","https://openalex.org/W1697075315","https://openalex.org/W1718360928","https://openalex.org/W1793835291","https://openalex.org/W1804110266","https://openalex.org/W1823551649","https://openalex.org/W1903347069","https://openalex.org/W1933990309","https://openalex.org/W1951629768","https://openalex.org/W1994666506","https://openalex.org/W1994719275","https://openalex.org/W2000157792","https://openalex.org/W2008732654","https://openalex.org/W2024254345","https://openalex.org/W2027982384","https://openalex.org/W2034683677","https://openalex.org/W2040055413","https://openalex.org/W2045512849","https://openalex.org/W2051237969","https://openalex.org/W2053885701","https://openalex.org/W2064404969","https://openalex.org/W2074859470","https://openalex.org/W2075184363","https://openalex.org/W2078397124","https://openalex.org/W2079135578","https://openalex.org/W2084653541","https://openalex.org/W2096295738","https://openalex.org/W2096613063","https://openalex.org/W2097607403","https://openalex.org/W2097612342","https://openalex.org/W2099210013","https://openalex.org/W2099741732","https://openalex.org/W2105459687","https://openalex.org/W2106005123","https://openalex.org/W2106037979","https://openalex.org/W2106334384","https://openalex.org/W2107411554","https://openalex.org/W2109999391","https://openalex.org/W2110451175","https://openalex.org/W2110662303","https://openalex.org/W2111604514","https://openalex.org/W2116840760","https://openalex.org/W2119385818","https://openalex.org/W2119787772","https://openalex.org/W2122738268","https://openalex.org/W2126464735","https://openalex.org/W2127114523","https://openalex.org/W2129732816","https://openalex.org/W2130800351","https://openalex.org/W2138967244","https://openalex.org/W2139158168","https://openalex.org/W2140867429","https://openalex.org/W2141224535","https://openalex.org/W2142949395","https://openalex.org/W2143859313","https://openalex.org/W2143915663","https://openalex.org/W2144006746","https://openalex.org/W2144730813","https://openalex.org/W2145889472","https://openalex.org/W2145962650","https://openalex.org/W2152046843","https://openalex.org/W2158746276","https://openalex.org/W2161219071","https://openalex.org/W2161305109","https://openalex.org/W2167077875","https://openalex.org/W2167349346","https://openalex.org/W2185602187","https://openalex.org/W2296319761","https://openalex.org/W2407000478","https://openalex.org/W2566608758","https://openalex.org/W2950289646","https://openalex.org/W2950618512","https://openalex.org/W2951713178","https://openalex.org/W2962737134","https://openalex.org/W2962959718","https://openalex.org/W2963641291","https://openalex.org/W2963684688","https://openalex.org/W3019202532","https://openalex.org/W3029645440","https://openalex.org/W4206310440","https://openalex.org/W4235713725","https://openalex.org/W4285719527","https://openalex.org/W6728508557","https://openalex.org/W6991389937","https://openalex.org/W7030295306","https://openalex.org/W7097492172"],"related_works":["https://openalex.org/W2601846890","https://openalex.org/W643635367","https://openalex.org/W2255205876","https://openalex.org/W2106334384","https://openalex.org/W4307074154","https://openalex.org/W7098324565","https://openalex.org/W2980956598","https://openalex.org/W2083493778","https://openalex.org/W2979666730","https://openalex.org/W3034685228"],"abstract_inverted_index":{"We":[0,33],"consider":[1],"the":[2,27,35,85,97,137],"problem":[3,141],"of":[4,30,87,96,142],"recovering":[5,143],"a":[6,76,93],"complete":[7],"(i.e.,":[8],"square":[9],"and":[10,79,136],"invertible)":[11],"dictionary":[12,31],"A0,":[13],"from":[14],"Y":[15,18],"=":[16],"A0X0with":[17],"\u03f5":[19],"Rn\u00d7p.":[20],"This":[21,113],"recovery":[22,58],"setting":[23],"is":[24,70,81],"central":[25],"to":[26],"theoretical":[28],"understanding":[29],"learning.":[32],"give":[34,92],"first":[36],"efficient":[37],"algorithm":[38,69],"that":[39,103],"provably":[40],"recovers":[41],"A0when":[42],"X0has":[43,61],"O":[44,63],"(n)":[45],"nonzeros":[46,65],"per":[47,66],"column,":[48],"under":[49],"suitable":[50],"probability":[51,106],"model":[52],"for":[53,130],"X0.":[54],"Prior":[55],"results":[56],"provide":[57],"guarantees":[59],"when":[60],"only":[62],"(\u221an)":[64],"column.":[67],"Our":[68,90],"based":[71],"on":[72],"nonconvex":[73],"optimization":[74],"with":[75,104,146],"spherical":[77],"constraint,":[78],"hence":[80],"naturally":[82],"phrased":[83],"in":[84,120,133],"language":[86],"manifold":[88],"optimization.":[89],"proofs":[91],"geometric":[94],"characterization":[95],"high-dimensional":[98],"objective":[99],"landscape,":[100],"which":[101],"shows":[102],"high":[105],"there":[107],"are":[108],"no":[109],"spurious":[110],"local":[111],"minima.":[112],"invited":[114],"talk":[115],"summarizes":[116],"these":[117],"results,":[118],"presented":[119],"[1].":[121],"It":[122],"also":[123],"presents":[124],"numerical":[125],"experiments":[126],"demonstrating":[127],"their":[128],"implications":[129],"practical":[131],"problems":[132],"representation":[134],"learning":[135],"more":[138],"general":[139],"algorithmic":[140],"matrix":[144],"decompositions":[145],"structured":[147],"factors.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":21},{"year":2015,"cited_by_count":9}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2019-07-30T00:00:00"}