{"id":"https://openalex.org/W2950919939","doi":"https://doi.org/10.1145/3174804","title":"A Faster Subquadratic Algorithm for Finding Outlier Correlations","display_name":"A Faster Subquadratic Algorithm for Finding Outlier Correlations","publication_year":2018,"publication_date":"2018-06-16","ids":{"openalex":"https://openalex.org/W2950919939","doi":"https://doi.org/10.1145/3174804","mag":"2950919939"},"language":"en","primary_location":{"id":"doi:10.1145/3174804","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3174804","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1145/3174804","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029115114","display_name":"Matti Karppa","orcid":"https://orcid.org/0000-0002-9381-8949"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Matti Karppa","raw_affiliation_strings":["Aalto University, Finland","Aalto University Helsinki, Finland#TAB#"],"affiliations":[{"raw_affiliation_string":"Aalto University, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Aalto University Helsinki, Finland#TAB#","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055721632","display_name":"Petteri Kaski","orcid":"https://orcid.org/0009-0002-3069-7753"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Petteri Kaski","raw_affiliation_strings":["Aalto University, Finland","Aalto University Helsinki, Finland#TAB#"],"affiliations":[{"raw_affiliation_string":"Aalto University, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Aalto University Helsinki, Finland#TAB#","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043404047","display_name":"Jukka Kohonen","orcid":"https://orcid.org/0000-0003-4859-1463"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Jukka Kohonen","raw_affiliation_strings":["Aalto University, Finland","Aalto University Helsinki, Finland#TAB#"],"affiliations":[{"raw_affiliation_string":"Aalto University, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Aalto University Helsinki, Finland#TAB#","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029115114"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2286874,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"3","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9969000220298767,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9969000220298767,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9969000220298767,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9904000163078308,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7970688343048096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6244073510169983},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6107908487319946},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5055139064788818},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.46790820360183716},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4511314630508423},{"id":"https://openalex.org/keywords/unit-vector","display_name":"Unit vector","score":0.429522842168808},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.42000359296798706},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3695112466812134},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24503648281097412},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1960846185684204}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7970688343048096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6244073510169983},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6107908487319946},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5055139064788818},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.46790820360183716},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4511314630508423},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.429522842168808},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.42000359296798706},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3695112466812134},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24503648281097412},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1960846185684204},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3174804","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3174804","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1510.03895","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.03895","pdf_url":"https://arxiv.org/pdf/1510.03895","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2950919939","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1510.03895.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1510.03895","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1510.03895","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1145/3174804","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3174804","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G2761285720","display_name":null,"funder_award_id":"FP/2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3981126665","display_name":null,"funder_award_id":"Seventh Framework Programme","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5593277320","display_name":null,"funder_award_id":"2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8841511727","display_name":"Theory and Practice of Advanced Search and Enumeration","funder_award_id":"338077","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":74,"referenced_works":["https://openalex.org/W73389528","https://openalex.org/W299839057","https://openalex.org/W566315627","https://openalex.org/W1430582609","https://openalex.org/W1455310343","https://openalex.org/W1488303220","https://openalex.org/W1541459201","https://openalex.org/W1562285034","https://openalex.org/W1581095529","https://openalex.org/W1599364940","https://openalex.org/W1647207848","https://openalex.org/W1915272284","https://openalex.org/W1968540673","https://openalex.org/W1977046819","https://openalex.org/W1978475816","https://openalex.org/W1985289891","https://openalex.org/W1985572324","https://openalex.org/W1986983672","https://openalex.org/W1991718539","https://openalex.org/W1995725694","https://openalex.org/W1997744504","https://openalex.org/W2002058256","https://openalex.org/W2002359780","https://openalex.org/W2010416066","https://openalex.org/W2012833704","https://openalex.org/W2017851434","https://openalex.org/W2028087580","https://openalex.org/W2042465463","https://openalex.org/W2048779798","https://openalex.org/W2050749090","https://openalex.org/W2061684784","https://openalex.org/W2063003848","https://openalex.org/W2065151783","https://openalex.org/W2065259291","https://openalex.org/W2075843680","https://openalex.org/W2080844740","https://openalex.org/W2084732238","https://openalex.org/W2086789740","https://openalex.org/W2094090625","https://openalex.org/W2097184821","https://openalex.org/W2097776316","https://openalex.org/W2100344784","https://openalex.org/W2103012681","https://openalex.org/W2114177725","https://openalex.org/W2120248756","https://openalex.org/W2121269638","https://openalex.org/W2121516976","https://openalex.org/W2123427850","https://openalex.org/W2123485784","https://openalex.org/W2125980212","https://openalex.org/W2127859122","https://openalex.org/W2128793454","https://openalex.org/W2145065594","https://openalex.org/W2147717514","https://openalex.org/W2151584222","https://openalex.org/W2163972006","https://openalex.org/W2169795703","https://openalex.org/W2201600774","https://openalex.org/W2206830592","https://openalex.org/W2218762779","https://openalex.org/W2261895596","https://openalex.org/W2263882035","https://openalex.org/W2401929940","https://openalex.org/W2546792675","https://openalex.org/W2949388608","https://openalex.org/W2951040528","https://openalex.org/W2962814541","https://openalex.org/W2962863202","https://openalex.org/W2963056065","https://openalex.org/W2963593740","https://openalex.org/W3093544618","https://openalex.org/W3105727767","https://openalex.org/W3141299647","https://openalex.org/W4233413206"],"related_works":["https://openalex.org/W3126682399","https://openalex.org/W2949099125","https://openalex.org/W2436227985","https://openalex.org/W2952501021","https://openalex.org/W1947158611","https://openalex.org/W3203900422","https://openalex.org/W2970165664","https://openalex.org/W2950284340","https://openalex.org/W2396944443","https://openalex.org/W3177083673","https://openalex.org/W3101125945","https://openalex.org/W2287138463","https://openalex.org/W2502975660","https://openalex.org/W3090172199","https://openalex.org/W2978789755","https://openalex.org/W2959998608","https://openalex.org/W2949921088","https://openalex.org/W2902005533","https://openalex.org/W3101350160","https://openalex.org/W3012317967"],"abstract_inverted_index":{"We":[0,285],"study":[1],"the":[2,29,66,83,166,250,261,290],"problem":[3,293],"of":[4,8,15,40,69,92,107],"detecting":[5],"outlier":[6,67],"pairs":[7,68,91],"strongly":[9],"correlated":[10],"variables":[11,17],"among":[12],"a":[13,38,116,157],"collection":[14],"n":[16,41,135,172,177,184,189,210,228,274],"with":[18,43,181],"otherwise":[19],"weak":[20],"pairwise":[21],"correlations.":[22],"After":[23],"normalization,":[24],"this":[25],"task":[26,31],"amounts":[27],"to":[28,63,82,127,168],"geometric":[30],"where":[32,152,245],"we":[33,60,114,200],"are":[34,61],"given":[35],"as":[36],"input":[37],"set":[39],"vectors":[42,70,93],"unit":[44,128],"Euclidean":[45,129],"norm":[46],"and":[47,51,161,193,223,256,275,283,294],"dimension":[48],"d":[49,276],",":[50],"for":[52,120,252,263,289,295],"some":[53],"constants":[54],"0&lt;\u03c4":[55],"&lt;":[56,58,154],"\u03c1":[57,77,214,221,282],"1,":[59],"asked":[62],"find":[64],"all":[65,86],"whose":[71,277],"inner":[72,95],"product":[73,96],"is":[74,156,165,249,260],"at":[75,88,97],"least":[76],"in":[78,100,132,206,224,273],"absolute":[79,101],"value,":[80],"subject":[81],"promise":[84],"that":[85,119,204],"but":[87],"most":[89,98],"q":[90],"have":[94],"\u03c4":[99,196,213,218,233,239,242],"value.":[102],"Improving":[103],"on":[104,281],"an":[105,170,182],"algorithm":[106,118],"Valiant":[108],"[FOCS":[109],"2012;":[110],"J.":[111],"ACM":[112],"2015],":[113],"present":[115,286],"randomized":[117,202],"Boolean":[121,298],"inputs":[122],"({":[123],"\u22121,1}-valued":[124],"data":[125],"normalized":[126],"length)":[130],"runs":[131],"time":[133,207,225],"\u00d5((":[134],"max,{":[136],"1\u2212\u03b3":[137],"+":[138,148,215,235],"M":[139,143,162],"(\u0394":[140],"\u03b3":[141],",\u03b3),":[142],"(1\u2212\u03b3":[144],",2":[145],"\u0394":[146,194],"\u03b3)}":[147],"qdn":[149,216,236],"2\u03b3":[150],"),":[151],"0&lt;\u03b3":[153],"1":[155,259],"constant":[158],"tradeoff":[159],"parameter":[160],"(\u03bc,":[163],"\u03bd)":[164],"exponent":[167,251,262],"multiply":[169],"\u230a":[171,176,183,188],"\u03bc":[173,190],"\u230b":[174,179,186,191],"\u00d7":[175,187],"\u03bd":[178,185],"matrix":[180,192,254,265],"=1/(1\u2212log":[195],"\u03c1).":[197],"As":[198],"corollaries":[199,288],"obtain":[201],"algorithms":[203],"run":[205],"\u00d5(":[208],"(":[209,227],"2/\u03c9":[211],"3\u2212log":[212],"2/(1\u2212log":[217],"\u03c1)3=log":[219],"\u03c4\u03c4":[220],")":[222],"\u00f5(":[226],"4":[229],"/":[230],"2+\u03b1":[231],"(1\u2212log":[232,238,241],"\u03c1)":[234,243],"2/\u03b1":[237],"\u03c1)2+\u03b1":[240],"&gt;),":[244],"2\u2264":[246],"\u03c9":[247],"&lt;2.38":[248],"square":[253],"multiplication":[255],"0.3&lt;\u03b1":[257],"\u2264":[258],"rectangular":[264],"multiplication.":[266],"The":[267],"notation":[268],"\u00d5(\u1e61)":[269],"hides":[270],"polylogarithmic":[271],"factors":[272],"degree":[278],"may":[279],"depend":[280],"\u03c4.":[284],"further":[287],"light":[291],"bulb":[292],"learning":[296],"sparse":[297],"functions.":[299]},"counts_by_year":[],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}
