{"id":"https://openalex.org/W2953276104","doi":"https://doi.org/10.1145/3302249","title":"Sparse Approximation via Generating Point Sets","display_name":"Sparse Approximation via Generating Point Sets","publication_year":2019,"publication_date":"2019-06-12","ids":{"openalex":"https://openalex.org/W2953276104","doi":"https://doi.org/10.1145/3302249","mag":"2953276104"},"language":"en","primary_location":{"id":"doi:10.1145/3302249","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3302249","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3302249","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3302249","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024803432","display_name":"Avrim Blum","orcid":"https://orcid.org/0000-0003-2450-5102"},"institutions":[{"id":"https://openalex.org/I160992636","display_name":"Toyota Technological Institute at Chicago","ror":"https://ror.org/02sn5gb64","country_code":"US","type":"education","lineage":["https://openalex.org/I160992636"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Avrim Blum","raw_affiliation_strings":["Toyota Technological Institute at Chicago, Chicago, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toyota Technological Institute at Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I160992636"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040577923","display_name":"Sariel Har-Peled","orcid":"https://orcid.org/0000-0003-2638-9635"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sariel Har-Peled","raw_affiliation_strings":["University of Illinois, Urbana-Champaign, Urbana, IL, USA","University of Illinois, Urbana?Champaign, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois, Urbana?Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054913384","display_name":"Benjamin Raichel","orcid":"https://orcid.org/0000-0001-6584-4843"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin Raichel","raw_affiliation_strings":["University of Texas at Dallas, Richardson, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Dallas, Richardson, TX, USA","institution_ids":["https://openalex.org/I162577319"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024803432"],"corresponding_institution_ids":["https://openalex.org/I160992636"],"apc_list":null,"apc_paid":null,"fwci":0.3883,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59168327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"15","issue":"3","first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9973999857902527,"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":0.9973999857902527,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.996999979019165,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9945999979972839,"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/convex-hull","display_name":"Convex hull","score":0.8986672163009644},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7414367198944092},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7251689434051514},{"id":"https://openalex.org/keywords/orthogonal-convex-hull","display_name":"Orthogonal convex hull","score":0.698441743850708},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.5560559034347534},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.545984148979187},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.5386040210723877},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.531886637210846},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5159736275672913},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5046647787094116},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.49032285809516907},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.48904523253440857},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.4321132302284241},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.42337071895599365},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41808587312698364},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2661277651786804},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1706913411617279},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14398646354675293}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.8986672163009644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7414367198944092},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7251689434051514},{"id":"https://openalex.org/C64051489","wikidata":"https://www.wikidata.org/wiki/Q7104528","display_name":"Orthogonal convex hull","level":5,"score":0.698441743850708},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.5560559034347534},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.545984148979187},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.5386040210723877},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.531886637210846},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5159736275672913},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5046647787094116},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.49032285809516907},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.48904523253440857},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.4321132302284241},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.42337071895599365},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41808587312698364},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2661277651786804},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1706913411617279},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14398646354675293}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3302249","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3302249","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3302249","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3302249","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3302249","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3302249","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G151214518","display_name":null,"funder_award_id":"CCF-1415460","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G179613736","display_name":"AF:  Small:  Towards better geometric algorithms: Summarizing, partitioning and shrinking data","funder_award_id":"1421231","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2111735816","display_name":"Eager: Discrete Optimization Algorithms for 21st Century Algorithms","funder_award_id":"1415460","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4218816690","display_name":"AF: Small: New Directions in Learning Theory","funder_award_id":"1525971","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6271038849","display_name":"AF: Small:  Efficient Proximity and Similarity Search in Computational Geometry","funder_award_id":"1217462","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G736274355","display_name":null,"funder_award_id":"CCF-1421231","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7421958168","display_name":"CAREER:  AF: Giving Form to Data with a Geometric Scaffold","funder_award_id":"1750780","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7679408513","display_name":null,"funder_award_id":"CCF-1415460,CCF-1525971,CCF-1421231,CCF-1217462","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7864877588","display_name":null,"funder_award_id":"CCF-1217462","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8779086508","display_name":"CRII: AF: Breaking Barriers for Geometric Data","funder_award_id":"1566137","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/F4320332222","display_name":"University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"},{"id":"https://openalex.org/F4320337517","display_name":"Graduate College, University of Illinois at Urbana-Champaign","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2953276104.pdf","grobid_xml":"https://content.openalex.org/works/W2953276104.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1560989141","https://openalex.org/W1581442026","https://openalex.org/W1973264045","https://openalex.org/W1981313592","https://openalex.org/W2054459484","https://openalex.org/W2109706083","https://openalex.org/W2200725028","https://openalex.org/W2247953682","https://openalex.org/W2596180971","https://openalex.org/W2953381419"],"related_works":["https://openalex.org/W2300145982","https://openalex.org/W2580512045","https://openalex.org/W2365830408","https://openalex.org/W1569666406","https://openalex.org/W2375652826","https://openalex.org/W2048874717","https://openalex.org/W981962503","https://openalex.org/W1500255470","https://openalex.org/W1758159897","https://openalex.org/W2371177213"],"abstract_inverted_index":{"For":[0],"a":[1,20,77,85,120,138,149,156],"set":[2],"P":[3,25,52,115],"of":[4,18,33,45,51,68,79,87,93,108,114,122,124,155,160],"n":[5],"points":[6,123],"in":[7,106,148,174],"the":[8,16,31,34,38,42,48,88,103,109,146,161,175],"unit":[9],"ball":[10],"b\u2286":[11],"R":[12],"d":[13,105],",":[14,72],"consider":[15],"problem":[17],"finding":[19],"small":[21,157],"subset":[22,158],"T":[23,46,125,159],"\u2286":[24],"such":[26,65,94],"that":[27,126],"its":[28],"convex-hull":[29,32],"\u03b5-approximates":[30],"original":[35,162,176],"set.":[36],"Specifically,":[37],"Hausdorff":[39],"distance":[40],"between":[41],"convex":[43,49,142],"hull":[44,50],"and":[47,81,170],"should":[53],"be":[54,117,135,168],"at":[55],"most":[56],"\u03b5.":[57],"We":[58],"present":[59],"an":[60,66,95],"efficient":[61],"algorithm":[62,166],"to":[63],"compute":[64],"\u03b5\u2032-approximation":[67],"size":[69,90],"k":[70,82,91],"alg":[71,83],"where":[73],"\u03b5":[74,80],"\u2032":[75],"is":[76,84,99,127],"function":[78,86],"minimum":[89],"opt":[92],"\u03b5-approximation.":[96],"Surprisingly,":[97],"there":[98],"no":[100],"dependence":[101],"on":[102],"dimension":[104],"either":[107],"bounds.":[110],"Furthermore,":[111],"every":[112],"point":[113],"can":[116,134,167],"\u03b5-approximated":[118],"by":[119],"convex-combination":[121],"O":[128],"(1/\u03b5":[129],"2":[130],")-sparse.":[131],"Our":[132],"result":[133],"viewed":[136],"as":[137],"method":[139],"for":[140],"sparse,":[141],"autoencoding:":[143],"approximately":[144],"representing":[145],"data":[147],"compact":[150],"way":[151],"using":[152],"sparse":[153],"combinations":[154],"data.":[163],"The":[164],"new":[165],"kernelized,":[169],"it":[171],"preserves":[172],"sparsity":[173],"input.":[177]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
