{"id":"https://openalex.org/W1903347069","doi":"https://doi.org/10.1109/tit.2015.2460238","title":"When Can Dictionary Learning Uniquely Recover Sparse Data From Subsamples?","display_name":"When Can Dictionary Learning Uniquely Recover Sparse Data From Subsamples?","publication_year":2015,"publication_date":"2015-07-23","ids":{"openalex":"https://openalex.org/W1903347069","doi":"https://doi.org/10.1109/tit.2015.2460238","mag":"1903347069"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2015.2460238","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2460238","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1106.3616","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Christopher J. Hillar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christopher J. Hillar","raw_affiliation_strings":["Redwood Center for Theoretical Neuroscience, University of California at Berkeley, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, University of California at Berkeley, Berkeley, CA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Friedrich T. Sommer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Friedrich T. Sommer","raw_affiliation_strings":["Redwood Center for Theoretical Neuroscience, University of California at Berkeley, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, University of California at Berkeley, Berkeley, CA, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8692,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.71650212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"61","issue":"11","first_page":"6290","last_page":"6297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.2791999876499176,"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":0.2791999876499176,"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/T12303","display_name":"Tensor decomposition and applications","score":0.2671000063419342,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.10779999941587448,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/neural-coding","display_name":"Neural coding","score":0.7936999797821045},{"id":"https://openalex.org/keywords/k-svd","display_name":"K-SVD","score":0.640500009059906},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.6398000121116638},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5496000051498413},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5059999823570251},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.47099998593330383},{"id":"https://openalex.org/keywords/dictionary-learning","display_name":"Dictionary learning","score":0.4133000075817108},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3896999955177307},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.38100001215934753}],"concepts":[{"id":"https://openalex.org/C77637269","wikidata":"https://www.wikidata.org/wiki/Q7002051","display_name":"Neural coding","level":2,"score":0.7936999797821045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.704200029373169},{"id":"https://openalex.org/C154771677","wikidata":"https://www.wikidata.org/wiki/Q17098361","display_name":"K-SVD","level":3,"score":0.640500009059906},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.6398000121116638},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5496000051498413},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5059999823570251},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.47290000319480896},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.47099998593330383},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4359999895095825},{"id":"https://openalex.org/C2988886741","wikidata":"https://www.wikidata.org/wiki/Q25304494","display_name":"Dictionary learning","level":3,"score":0.4133000075817108},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.40290001034736633},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.38100001215934753},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.29350000619888306},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C195324797","wikidata":"https://www.wikidata.org/wiki/Q33742","display_name":"Natural language","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C2781170535","wikidata":"https://www.wikidata.org/wiki/Q30587856","display_name":"Noisy data","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2015.2460238","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2460238","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1106.3616","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1106.3616","pdf_url":"https://arxiv.org/pdf/1106.3616","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1106.3616","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1106.3616","pdf_url":"https://arxiv.org/pdf/1106.3616","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":[{"id":"https://openalex.org/G1799333409","display_name":null,"funder_award_id":"DE-AC02-05CH11231","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G8169460767","display_name":null,"funder_award_id":"NSF-0855272","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8984359682","display_name":null,"funder_award_id":"NSF-1219212","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/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1971027050","https://openalex.org/W1975612794","https://openalex.org/W1991693778","https://openalex.org/W2030449718","https://openalex.org/W2037783071","https://openalex.org/W2045472305","https://openalex.org/W2078204800","https://openalex.org/W2082633388","https://openalex.org/W2084357816","https://openalex.org/W2090042335","https://openalex.org/W2099741732","https://openalex.org/W2100502520","https://openalex.org/W2101933716","https://openalex.org/W2108384452","https://openalex.org/W2111790388","https://openalex.org/W2115205382","https://openalex.org/W2122741244","https://openalex.org/W2127114523","https://openalex.org/W2129131372","https://openalex.org/W2133285226","https://openalex.org/W2137234026","https://openalex.org/W2145889472","https://openalex.org/W2150409012","https://openalex.org/W2155981690","https://openalex.org/W2168537135","https://openalex.org/W2170962921","https://openalex.org/W2951417773","https://openalex.org/W3022436500","https://openalex.org/W4250955649","https://openalex.org/W6603855813","https://openalex.org/W6629304500","https://openalex.org/W6674642818","https://openalex.org/W6675992869","https://openalex.org/W6676454372","https://openalex.org/W6676727762","https://openalex.org/W6677725119","https://openalex.org/W6682256868","https://openalex.org/W6682411926","https://openalex.org/W6686418764","https://openalex.org/W6714134332"],"related_works":[],"abstract_inverted_index":{"Sparse":[0],"coding":[1],"or":[2],"sparse":[3,33,99],"dictionary":[4],"learning":[5,88],"has":[6],"been":[7],"widely":[8],"used":[9],"to":[10,40,57,79,108],"recover":[11],"underlying":[12],"structure":[13],"in":[14,50,92],"many":[15],"kinds":[16],"of":[17,81],"natural":[18,41],"data.":[19],"Here,":[20],"we":[21],"provide":[22],"conditions":[23,78],"guaranteeing":[24,64],"when":[25,32],"this":[26],"recovery":[27],"is":[28,46],"universal;":[29],"that":[30,54,90],"is,":[31],"codes":[34,100],"and":[35,101,110],"dictionaries":[36],"are":[37,74,84],"unique":[38],"(up":[39],"symmetries).":[42],"Our":[43],"main":[44],"tool":[45],"a":[47],"useful":[48],"lemma":[49],"combinatorial":[51],"matrix":[52],"theory":[53],"allows":[55],"us":[56],"derive":[58],"bounds":[59],"on":[60],"the":[61,77,94,97],"sample":[62],"sizes":[63],"such":[65],"uniqueness":[66],"under":[67],"various":[68],"assumptions":[69],"for":[70],"how":[71],"training":[72],"data":[73,95,111],"generated.":[75],"Whenever":[76],"one":[80],"our":[82],"theorems":[83],"met,":[85],"any":[86],"sparsity-constrained":[87],"algorithm":[89],"succeeds":[91],"reconstructing":[93],"recovers":[96],"original":[98],"dictionary.":[102],"We":[103],"also":[104],"discuss":[105],"potential":[106],"applications":[107],"neuroscience":[109],"analysis.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2016-06-24T00:00:00"}