{"id":"https://openalex.org/W4211053519","doi":"https://doi.org/10.1137/1.9781611973082.69","title":"A Nonlinear Approach to Dimension Reduction","display_name":"A Nonlinear Approach to Dimension Reduction","publication_year":2011,"publication_date":"2011-01-23","ids":{"openalex":"https://openalex.org/W4211053519","doi":"https://doi.org/10.1137/1.9781611973082.69"},"language":"en","primary_location":{"id":"doi:10.1137/1.9781611973082.69","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611973082.69","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"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/A5057494907","display_name":"Lee-Ad Gottlieb","orcid":"https://orcid.org/0000-0003-3355-351X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee-Ad Gottlieb","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037378898","display_name":"Robert Krauthgamer","orcid":"https://orcid.org/0009-0003-8154-3735"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Krauthgamer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1582,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.89276881,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"888","last_page":"899"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9933000206947327,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9933000206947327,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9833999872207642,"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/dimension","display_name":"Dimension (graph theory)","score":0.6737560033798218},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5682201981544495},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5306099057197571},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5272998809814453},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.48522424697875977},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.467507928609848},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44910499453544617},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.448678195476532},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.442666620016098},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43698030710220337},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41882482171058655},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39230453968048096},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13876456022262573},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1377270221710205},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09049391746520996}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6737560033798218},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5682201981544495},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5306099057197571},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5272998809814453},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.48522424697875977},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.467507928609848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44910499453544617},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.448678195476532},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.442666620016098},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43698030710220337},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41882482171058655},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39230453968048096},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13876456022262573},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1377270221710205},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09049391746520996},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/1.9781611973082.69","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611973082.69","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2949964783","https://openalex.org/W2768610039","https://openalex.org/W3121250382","https://openalex.org/W4285390085","https://openalex.org/W31688704","https://openalex.org/W2801357573","https://openalex.org/W2974000959","https://openalex.org/W2106889256"],"abstract_inverted_index":{"The":[0,74],"\u21132":[1,84],"flattening":[2],"lemma":[3],"of":[4,32,36,72,78,104],"Johnson":[5],"and":[6,28,52,61,122,130],"Lindenstrauss":[7],"[JL84]":[8],"is":[9,62,112],"a":[10,79],"powerful":[11],"tool":[12],"for":[13,94,142],"dimension":[14,23,95,111,134],"reduction.":[15],"It":[16],"has":[17],"been":[18],"conjectured":[19],"that":[20,97],"the":[21,33,37,42,101,105,109,115,125,133],"target":[22,110],"bounds":[24,135],"can":[25,85],"be":[26,86],"refined":[27],"bounded":[29],"in":[30,69,114],"terms":[31],"intrinsic":[34],"dimensionality":[35],"data":[38],"set":[39,81],"(for":[40],"example,":[41],"doubling":[43,80,102,116],"dimension).":[44],"One":[45],"such":[46],"problem":[47],"was":[48],"proposed":[49],"by":[50],"Lang":[51],"Plaut":[53],"[LP01]":[54],"(see":[55],"also":[56],"[GKL03,":[57],"Mat02,":[58],"ABN08,":[59],"CGT10]),":[60],"still":[63],"open.":[64],"We":[65],"prove":[66],"another":[67],"result":[68],"this":[70],"line":[71],"work:":[73],"snowflake":[75],"metric":[76],"d1/2":[77],"S":[82],"\u2282":[83],"embedded":[87],"with":[88],"arbitrarily":[89],"low":[90],"distortion":[91],"into":[92],"\u2113D2,":[93],"D":[96],"depends":[98],"solely":[99],"on":[100],"constant":[103],"metric.":[106],"In":[107],"fact,":[108],"polylogarithmic":[113],"constant.":[117],"Our":[118],"techniques":[119],"are":[120,137],"robust":[121],"extend":[123],"to":[124],"more":[126],"difficult":[127],"spaces":[128],"\u21131":[129],"\u2113\u221e,":[131],"although":[132],"here":[136],"quantitatively":[138],"inferior":[139],"than":[140],"those":[141],"\u21132.":[143]},"counts_by_year":[{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
