{"id":"https://openalex.org/W2553632983","doi":"https://doi.org/10.1137/15m1047921","title":"Stratifying High-Dimensional Data Based on Proximity to the Convex Hull Boundary","display_name":"Stratifying High-Dimensional Data Based on Proximity to the Convex Hull Boundary","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2553632983","doi":"https://doi.org/10.1137/15m1047921","mag":"2553632983"},"language":"en","primary_location":{"id":"doi:10.1137/15m1047921","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1047921","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1047921","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1047921","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043121321","display_name":"Lori Ziegelmeier","orcid":"https://orcid.org/0000-0002-1544-4937"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lori Ziegelmeier","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061567476","display_name":"Michael Kirby","orcid":"https://orcid.org/0000-0001-9802-9263"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Kirby","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078621088","display_name":"Chris Peterson","orcid":"https://orcid.org/0000-0002-3982-6876"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chris Peterson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5043121321"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1877,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.78978134,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"59","issue":"2","first_page":"346","last_page":"365"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9951000213623047,"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":0.8328818082809448},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6391003727912903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5993800163269043},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5707199573516846},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.5401939153671265},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5220208764076233},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5154362916946411},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4979982376098633},{"id":"https://openalex.org/keywords/data-point","display_name":"Data point","score":0.4928569793701172},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4687782824039459},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4674810767173767},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.4617713689804077},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.4605526030063629},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.43691179156303406},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.43359896540641785},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31823185086250305},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31757134199142456},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2619604468345642},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.21914812922477722},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.09235110878944397}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.8328818082809448},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6391003727912903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5993800163269043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5707199573516846},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.5401939153671265},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5220208764076233},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5154362916946411},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4979982376098633},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.4928569793701172},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4687782824039459},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4674810767173767},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.4617713689804077},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.4605526030063629},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.43691179156303406},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.43359896540641785},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31823185086250305},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31757134199142456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2619604468345642},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.21914812922477722},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.09235110878944397},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1047921","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1047921","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1047921","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/15m1047921","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1047921","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1047921","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6200000047683716}],"awards":[{"id":"https://openalex.org/G6515981281","display_name":null,"funder_award_id":"DMS-1228308","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2553632983.pdf","grobid_xml":"https://content.openalex.org/works/W2553632983.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1571966798","https://openalex.org/W1998700518","https://openalex.org/W2053186076","https://openalex.org/W2109006918","https://openalex.org/W2113399154","https://openalex.org/W2122825543","https://openalex.org/W2142058898","https://openalex.org/W2145096794","https://openalex.org/W2150500908","https://openalex.org/W2153504150","https://openalex.org/W2332151900","https://openalex.org/W4253763636","https://openalex.org/W4292363360"],"related_works":["https://openalex.org/W2300145982","https://openalex.org/W2375652826","https://openalex.org/W2363904277","https://openalex.org/W981962503","https://openalex.org/W2580512045","https://openalex.org/W2578380588","https://openalex.org/W1569666406","https://openalex.org/W2038488337","https://openalex.org/W2371177213","https://openalex.org/W3106007480"],"abstract_inverted_index":{"The":[0,127],"convex":[1,65,90,125],"hull":[2],"of":[3,6,14,23,33,53,63,75,88,123,129,144,154],"a":[4,69,79,96,141,162],"set":[5,38],"points,":[7],"$C$,":[8],"serves":[9],"to":[10,44,49,57,85,101,120],"expose":[11],"extremal":[12],"properties":[13],"$C$":[15,22],"and":[16,139,146],"can":[17,133,166],"help":[18],"identify":[19],"elements":[20],"in":[21,30,78,137],"high":[24,54],"interest.":[25],"For":[26,92],"many":[27],"problems,":[28],"particularly":[29],"the":[31,35,51,61,64,73,86,89,110,117,121,124,130,150,155],"presence":[32],"noise,":[34],"true":[36],"vertex":[37],"(and":[39],"facets)":[40],"may":[41],"be":[42,134,167],"difficult":[43],"determine.":[45],"One":[46],"solution":[47],"is":[48,99],"expand":[50],"list":[52],"interest":[55],"candidates":[56],"points":[58,77,145],"lying":[59],"near":[60],"boundary":[62,87,122],"hull.":[66,91,126],"We":[67,107],"propose":[68],"quadratic":[70,97],"program":[71,98],"for":[72,140],"purpose":[74],"stratifying":[76],"data":[80,94,173],"cloud":[81],"based":[82],"on":[83,169],"proximity":[84],"each":[93],"point,":[95],"solved":[100],"determine":[102],"an":[103],"associated":[104],"weight":[105,111,131],"vector.":[106],"show":[108],"that":[109],"vector":[112],"encodes":[113],"geometric":[114],"information":[115],"concerning":[116],"point's":[118],"relationship":[119],"computation":[128],"vectors":[132],"carried":[135],"out":[136],"parallel,":[138],"fixed":[142,147],"number":[143],"neighborhood":[148],"size,":[149],"overall":[151],"computational":[152],"complexity":[153],"algorithm":[156],"grows":[157],"linearly":[158],"with":[159],"dimension.":[160],"As":[161],"consequence,":[163],"meaningful":[164],"computations":[165],"completed":[168],"reasonably":[170],"large,":[171],"high-dimensional":[172],"sets.":[174]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}