{"id":"https://openalex.org/W4391732389","doi":"https://doi.org/10.1145/3647642","title":"nSimplex Zen : A Novel Dimensionality Reduction for Euclidean and Hilbert Spaces","display_name":"nSimplex Zen : A Novel Dimensionality Reduction for Euclidean and Hilbert Spaces","publication_year":2024,"publication_date":"2024-02-10","ids":{"openalex":"https://openalex.org/W4391732389","doi":"https://doi.org/10.1145/3647642"},"language":"en","primary_location":{"id":"doi:10.1145/3647642","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3647642","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"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 Knowledge Discovery from Data","raw_type":"journal-article"},"type":"article","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/A5048202050","display_name":"Richard Connor","orcid":"https://orcid.org/0000-0003-4734-8103"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Richard Connor","raw_affiliation_strings":["University of St Andrews, St Andrews, UK"],"raw_orcid":"https://orcid.org/0000-0003-4734-8103","affiliations":[{"raw_affiliation_string":"University of St Andrews, St Andrews, UK","institution_ids":["https://openalex.org/I16835326"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072640757","display_name":"Lucia Vadicamo","orcid":"https://orcid.org/0000-0001-7182-7038"},"institutions":[{"id":"https://openalex.org/I122991210","display_name":"Istituto di Scienza e Tecnologie dell'Informazione \"Alessandro Faedo\"","ror":"https://ror.org/05kacka20","country_code":"IT","type":"facility","lineage":["https://openalex.org/I122991210","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lucia Vadicamo","raw_affiliation_strings":["CNR-ISTI, Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7182-7038","affiliations":[{"raw_affiliation_string":"CNR-ISTI, Pisa, Italy","institution_ids":["https://openalex.org/I122991210"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6185,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62478593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"18","issue":"6","first_page":"1","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9932000041007996,"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/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.7708079814910889},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7465876340866089},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5865915417671204},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.570285975933075},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5541462898254395},{"id":"https://openalex.org/keywords/multidimensional-scaling","display_name":"Multidimensional scaling","score":0.547321617603302},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5219837427139282},{"id":"https://openalex.org/keywords/distance-matrix","display_name":"Distance matrix","score":0.5165952444076538},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5109938383102417},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.45670342445373535},{"id":"https://openalex.org/keywords/euclidean-distance-matrix","display_name":"Euclidean distance matrix","score":0.45307374000549316},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4401710331439972},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4106346368789673},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3990951180458069},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3524901270866394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2968711853027344},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2678554952144623},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.225882887840271},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19516217708587646},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12022501230239868}],"concepts":[{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.7708079814910889},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465876340866089},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5865915417671204},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.570285975933075},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5541462898254395},{"id":"https://openalex.org/C91682802","wikidata":"https://www.wikidata.org/wiki/Q620538","display_name":"Multidimensional scaling","level":2,"score":0.547321617603302},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5219837427139282},{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.5165952444076538},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5109938383102417},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.45670342445373535},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.45307374000549316},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4401710331439972},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4106346368789673},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3990951180458069},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3524901270866394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2968711853027344},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2678554952144623},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.225882887840271},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19516217708587646},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12022501230239868},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3647642","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3647642","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"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 Knowledge Discovery from Data","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W299839057","https://openalex.org/W1494380125","https://openalex.org/W1540596182","https://openalex.org/W1566135517","https://openalex.org/W2001141328","https://openalex.org/W2015777397","https://openalex.org/W2038044292","https://openalex.org/W2053171205","https://openalex.org/W2071128523","https://openalex.org/W2082941884","https://openalex.org/W2097117768","https://openalex.org/W2105572632","https://openalex.org/W2124386111","https://openalex.org/W2124509324","https://openalex.org/W2130221251","https://openalex.org/W2143331230","https://openalex.org/W2152825437","https://openalex.org/W2155803963","https://openalex.org/W2167816765","https://openalex.org/W2187089797","https://openalex.org/W2250384498","https://openalex.org/W2294798173","https://openalex.org/W2304387544","https://openalex.org/W2325868261","https://openalex.org/W2400089876","https://openalex.org/W2511351367","https://openalex.org/W2523544977","https://openalex.org/W2532189199","https://openalex.org/W2558748708","https://openalex.org/W2736398808","https://openalex.org/W2889326414","https://openalex.org/W2951831793","https://openalex.org/W2963964051","https://openalex.org/W2969833941","https://openalex.org/W2975012430","https://openalex.org/W3005676914","https://openalex.org/W3037749269","https://openalex.org/W3095542606","https://openalex.org/W4211232926","https://openalex.org/W4213009331","https://openalex.org/W4248108185","https://openalex.org/W4254491045","https://openalex.org/W4297440395","https://openalex.org/W4386886797","https://openalex.org/W6681499959"],"related_works":["https://openalex.org/W4294328694","https://openalex.org/W2908582041","https://openalex.org/W1997141628","https://openalex.org/W2085867756","https://openalex.org/W2296912420","https://openalex.org/W2348550256","https://openalex.org/W2171944046","https://openalex.org/W2026338131","https://openalex.org/W2591878960","https://openalex.org/W3135432081"],"abstract_inverted_index":{"Dimensionality":[0],"reduction":[1,199],"techniques":[2,33],"map":[3],"values":[4],"from":[5],"a":[6,13,19,28,88,125],"high":[7],"dimensional":[8],"space":[9,20,43],"to":[10,50,102,116,155,158,183,200],"one":[11],"with":[12,48,198],"lower":[14,89],"dimension.":[15],"The":[16,145],"result":[17],"is":[18],"which":[21],"requires":[22],"less":[23],"physical":[24],"memory":[25],"and":[26,69,80,111,161,171],"has":[27],"faster":[29],"distance":[30],"calculation.":[31],"These":[32],"are":[34],"widely":[35],"used":[36],"where":[37],"required":[38],"properties":[39,185,194],"of":[40,91,129,147,186],"the":[41,51,108,142,153],"reduced-dimension":[42],"give":[44],"an":[45],"acceptable":[46],"accuracy":[47],"respect":[49],"original":[52,143],"space.":[53,93,144],"Many":[54],"such":[55,74,96,106],"transforms":[56,86],"have":[57,61],"been":[58,62],"described.":[59],"They":[60],"classified":[63],"in":[64,141,178],"two":[65],"main":[66],"groups:":[67],"linear":[68],"topological":[70,127],".":[71],"Linear":[72],"methods":[73,95],"as":[75,97,107],"Principal":[76],"Component":[77],"Analysis":[78],"(PCA)":[79],"Random":[81],"Projection":[82],"(RP)":[83],"define":[84],"matrix-based":[85],"into":[87],"dimension":[90],"Euclidean":[92,160],"Topological":[94],"Multidimensional":[98],"Scaling":[99],"(MDS)":[100],"attempt":[101],"preserve":[103],"higher-level":[104],"aspects":[105],"nearest-neighbour":[109],"relation,":[110],"some":[112],"may":[113],"be":[114,156],"applied":[115,157],"non-Euclidean":[117],"spaces.":[118],"Here,":[119],"we":[120],"introduce":[121],"nSimplex":[122],"Zen":[123],",":[124],"novel":[126],"method":[128],"reducing":[130],"dimensionality.":[131],"Like":[132],"MDS,":[133],"it":[134],"relies":[135],"only":[136],"upon":[137],"pairwise":[138],"distances":[139],"measured":[140],"use":[146],"distances,":[148],"rather":[149],"than":[150,195],"coordinates,":[151],"allows":[152],"technique":[154,191],"both":[159],"other":[162],"Hilbert":[163],"spaces,":[164,188],"including":[165],"those":[166],"governed":[167],"by":[168],"Cosine,":[169],"Jensen\u2013Shannon":[170],"Quadratic":[172],"Form":[173],"distances.":[174],"We":[175],"show":[176],"that":[177],"almost":[179],"all":[180],"cases,":[181],"due":[182],"geometric":[184],"high-dimensional":[187],"our":[189],"new":[190],"gives":[192],"better":[193],"others,":[196],"especially":[197],"very":[201],"low":[202],"dimensions.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2024-02-11T00:00:00"}