{"id":"https://openalex.org/W2259682197","doi":null,"title":"Density corrected sparse recovery when R.I.P. condition is broken","display_name":"Density corrected sparse recovery when R.I.P. condition is broken","publication_year":2015,"publication_date":"2015-07-25","ids":{"openalex":"https://openalex.org/W2259682197","mag":"2259682197"},"language":"en","primary_location":{"id":"mag:2259682197","doi":null,"is_oa":false,"landing_page_url":"https://ijcai.org/Proceedings/15/Papers/515.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306419142","display_name":"International Conference on Artificial Intelligence","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":null,"is_accepted":false,"is_published":false,"raw_source_name":"International Conference on Artificial Intelligence","raw_type":null},"volume":null,"type":"conference-paper","is_traditional":true,"indexed_in":[],"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/A5101677851","display_name":"Ming Lin","orcid":"https://orcid.org/0000-0002-5741-0516","observed_orcids":["https://orcid.org/0000-0002-5741-0516"]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ming Lin","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA"],"raw_orcid":"https://orcid.org/0000-0002-5741-0516","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055927243","display_name":"Zhengzhong Lan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhengzhong Lan","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107836252","display_name":"Alexander G. Hauptmann","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander G. Hauptmann","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3664","last_page":"3670"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9955999851226807,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9955999851226807,"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/T10136","display_name":"Statistical Methods and Inference","score":0.003700000001117587,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/sparse-signal-recovery","display_name":"sparse signal recovery","score":0.9760000109672546},{"id":"https://openalex.org/keywords/density-correction","display_name":"density correction","score":0.6959999799728394},{"id":"https://openalex.org/keywords/correlated-features","display_name":"correlated features","score":0.703000009059906},{"id":"https://openalex.org/keywords/cluster-structure","display_name":"cluster structure","score":0.753000020980835},{"id":"https://openalex.org/keywords/consistent-estimation","display_name":"consistent estimation","score":0.7049999833106995},{"id":"https://openalex.org/keywords/geometric-convergence","display_name":"geometric convergence","score":0.7009999752044678}],"concepts":[{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.6995517611503601},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6846954822540283},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5350592732429504},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5071673393249512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48598799109458923},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4823710024356842},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.47402411699295044},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.4566355049610138},{"id":"https://openalex.org/C83665646","wikidata":"https://www.wikidata.org/wiki/Q42139305","display_name":"Feature vector","level":2,"score":0.43832215666770935},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43416187167167664},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4329807460308075},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34078699350357056},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20956951379776},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2091740369796753},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1322265863418579},{"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2259682197","doi":null,"is_oa":false,"landing_page_url":"https://ijcai.org/Proceedings/15/Papers/515.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306419142","display_name":"International Conference on Artificial Intelligence","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":null,"is_accepted":false,"is_published":false,"raw_source_name":"International Conference on Artificial Intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W54422097","https://openalex.org/W119997944","https://openalex.org/W153241469","https://openalex.org/W841113906","https://openalex.org/W1648884448","https://openalex.org/W1900913856","https://openalex.org/W1965193428","https://openalex.org/W1969048569","https://openalex.org/W1977520307","https://openalex.org/W1978593362","https://openalex.org/W1980454827","https://openalex.org/W1986046400","https://openalex.org/W1988946738","https://openalex.org/W1996777495","https://openalex.org/W2015881065","https://openalex.org/W2025079166","https://openalex.org/W2066986830","https://openalex.org/W2092058109","https://openalex.org/W2099210013","https://openalex.org/W2107411554","https://openalex.org/W2110057628","https://openalex.org/W2113346187","https://openalex.org/W2122825543","https://openalex.org/W2127271355","https://openalex.org/W2129016596","https://openalex.org/W2135046866","https://openalex.org/W2136758284","https://openalex.org/W2137198385","https://openalex.org/W2145096794","https://openalex.org/W2151103935","https://openalex.org/W2168909589","https://openalex.org/W2394655774","https://openalex.org/W2616050959","https://openalex.org/W2619994414","https://openalex.org/W2950933264","https://openalex.org/W2963172671","https://openalex.org/W2963322354","https://openalex.org/W2963765119"],"related_works":["https://openalex.org/W1798097147","https://openalex.org/W2804254801","https://openalex.org/W101277982","https://openalex.org/W7098956689","https://openalex.org/W7097232212","https://openalex.org/W2211942840","https://openalex.org/W2760700656","https://openalex.org/W7095644113","https://openalex.org/W2659595769","https://openalex.org/W2963995929"],"abstract_inverted_index":{"The":[0,88,108],"Restricted":[1],"Isometric":[2],"Property":[3],"(R.I.P.)":[4],"is":[5,62,122,127],"a":[6],"very":[7],"important":[8],"condition":[9],"for":[10],"recovering":[11],"sparse":[12,54,85],"vectors":[13],"from":[14,91],"high":[15],"dimensional":[16],"space.":[17],"Traditional":[18],"methods":[19],"often":[20,34,74],"rely":[21],"on":[22],"R.I.P":[23],"or":[24],"its":[25],"relaxed":[26],"variants.":[27],"However,":[28],"in":[29,57,76],"real":[30,77],"applications,":[31,78],"features":[32,69],"are":[33,80],"correlated":[35],"to":[36,45,82],"each":[37],"other,":[38],"which":[39,58,73,97],"makes":[40],"these":[41],"assumptions":[42],"too":[43],"strong":[44],"be":[46],"useful.":[47],"In":[48],"this":[49],"paper,":[50],"we":[51,79],"study":[52],"the":[53,59,84,99,123,128],"recovery":[55,116],"problem":[56],"feature":[60],"matrix":[61],"strictly":[63],"non-R.I.P.":[64],"We":[65],"prove":[66],"that":[67],"when":[68],"exhibit":[70],"cluster":[71,103,106],"structures,":[72],"happens":[75],"able":[81],"recover":[83],"vector":[86],"consistently.":[87],"consistency":[89],"comes":[90],"our":[92],"proposed":[93,109],"density":[94],"correction":[95],"algorithm,":[96],"removes":[98],"variance":[100],"of":[101],"estimated":[102],"centers":[104],"using":[105],"density.":[107],"algorithm":[110],"converges":[111],"geometrically,":[112],"achieves":[113],"nearly":[114],"optimal":[115],"bound":[117],"O(s2":[118],"log(d))":[119],"where":[120],"s":[121],"sparsity":[124],"and":[125],"d":[126],"nominal":[129],"dimension.":[130]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}