{"id":"https://openalex.org/W3012533921","doi":"https://doi.org/10.1109/cdc40024.2019.9030084","title":"Using SDP to Parameterize Universal Kernel Functions","display_name":"Using SDP to Parameterize Universal Kernel Functions","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W3012533921","doi":"https://doi.org/10.1109/cdc40024.2019.9030084","mag":"3012533921"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9030084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5025576040","display_name":"Brendon K. Colbert","orcid":"https://orcid.org/0000-0003-1580-555X"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Brendon K. Colbert","raw_affiliation_strings":["Department of Mechanical Engineering, Arizona State University, Tempe, AZ, US"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Arizona State University, Tempe, AZ, US","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077552862","display_name":"Matthew M. Peet","orcid":"https://orcid.org/0000-0001-9360-6738"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew M. Peet","raw_affiliation_strings":["Faculty of Mechanical Engineering, Arizona State University, Tempe, AZ, US"],"affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering, Arizona State University, Tempe, AZ, US","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025576040"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19257248,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4622","last_page":"4629"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9983999729156494,"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/T10057","display_name":"Face and Expression Recognition","score":0.9983999729156494,"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/T10320","display_name":"Neural Networks and Applications","score":0.9940000176429749,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9789000153541565,"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/kernel","display_name":"Kernel (algebra)","score":0.6331140995025635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6295904517173767},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.5765615105628967},{"id":"https://openalex.org/keywords/radial-basis-function-kernel","display_name":"Radial basis function kernel","score":0.5143455266952515},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.5023322105407715},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4801482558250427},{"id":"https://openalex.org/keywords/gaussian-function","display_name":"Gaussian function","score":0.47989094257354736},{"id":"https://openalex.org/keywords/tree-kernel","display_name":"Tree kernel","score":0.47973600029945374},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.47965219616889954},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.4495835602283478},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4440816044807434},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.4336654841899872},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36429286003112793},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3590737283229828},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.254158079624176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07412722706794739}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6331140995025635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6295904517173767},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.5765615105628967},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"score":0.5143455266952515},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.5023322105407715},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4801482558250427},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.47989094257354736},{"id":"https://openalex.org/C140417398","wikidata":"https://www.wikidata.org/wiki/Q16933942","display_name":"Tree kernel","level":5,"score":0.47973600029945374},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.47965219616889954},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.4495835602283478},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4440816044807434},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.4336654841899872},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36429286003112793},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3590737283229828},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.254158079624176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07412722706794739},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc40024.2019.9030084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.75,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W50076749","https://openalex.org/W1494236600","https://openalex.org/W1560724230","https://openalex.org/W1571024744","https://openalex.org/W1574617701","https://openalex.org/W1963905453","https://openalex.org/W1966805857","https://openalex.org/W1976079383","https://openalex.org/W2012110988","https://openalex.org/W2016990905","https://openalex.org/W2083496527","https://openalex.org/W2099693464","https://openalex.org/W2109743529","https://openalex.org/W2145295623","https://openalex.org/W2146722014","https://openalex.org/W2164535072","https://openalex.org/W2164943005","https://openalex.org/W2170356051","https://openalex.org/W2477133021","https://openalex.org/W2568793017","https://openalex.org/W2695777493","https://openalex.org/W2913243980","https://openalex.org/W3144619878","https://openalex.org/W6601962754","https://openalex.org/W6629626030","https://openalex.org/W6633893416","https://openalex.org/W6641446668","https://openalex.org/W6675004025","https://openalex.org/W6684067080","https://openalex.org/W6685016619","https://openalex.org/W6758804334"],"related_works":["https://openalex.org/W3013206934","https://openalex.org/W4221107122","https://openalex.org/W3100948281","https://openalex.org/W1535136526","https://openalex.org/W2005311689","https://openalex.org/W2353199197","https://openalex.org/W2382704364","https://openalex.org/W2558026684","https://openalex.org/W2366185040","https://openalex.org/W4375846106"],"abstract_inverted_index":{"We":[0,18],"propose":[1],"a":[2,11,82,99,139],"new":[3],"class":[4,24],"of":[5,22,62,74,116,135,162,165],"universal":[6,90],"kernel":[7,121,123],"functions":[8,48],"which":[9,102],"admit":[10],"linear":[12],"parametrization":[13],"using":[14],"positive":[15],"semidefinite":[16],"matrices.":[17],"refer":[19],"to":[20,30,36,65,168],"kernels":[21,131],"this":[23],"as":[25,198],"Tessellated":[26],"Kernels":[27],"(TKs)":[28],"due":[29],"the":[31,40,57,72,87,92,95,114,120,127,160,163,172,182],"observation":[32],"that":[33,94,113,158],"if":[34],"applied":[35],"kernel-based":[37],"learning":[38,119,181],"algorithms,":[39],"resulting":[41,96],"discriminants":[42,97],"are":[43,54,89],"defined":[44],"by":[45,56,71],"continuous":[46],"piecewise-polynomial":[47],"with":[49,190],"hyper-rectangular":[50],"domains":[51],"whose":[52],"vertices":[53],"determined":[55,70],"training":[58,166],"data.":[59],"The":[60],"number":[61,164],"parameters":[63],"used":[64],"define":[66],"these":[67],"TKs":[68,88,117,185],"is":[69,103,170],"length":[73],"an":[75],"associated":[76,133],"monomial":[77,84],"basis.":[78],"However,":[79],"even":[80],"for":[81,118,129,180],"single":[83],"basis":[85],"function":[86],"in":[91,105],"sense":[93],"occupy":[98],"hypothesis":[100],"space":[101],"dense":[104],"L":[106],"<sub":[107],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[108],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[109],".":[110],"This":[111],"implies":[112],"use":[115],"(aka":[122],"learning)":[124],"can":[125,186],"obviate":[126],"need":[128],"Gaussian":[130],"and":[132],"problem":[134],"selecting":[136],"bandwidth":[137],"-":[138],"conclusion":[140],"verified":[141],"through":[142],"extensive":[143],"numerical":[144],"testing":[145],"on":[146],"soft":[147],"margin":[148],"Support":[149],"Vector":[150],"Machine":[151],"(SVM)":[152],"problems.":[153],"Furthermore,":[154],"our":[155],"results":[156],"show":[157],"when":[159],"ratio":[161],"data":[167],"features":[169],"high,":[171],"proposed":[173],"method":[174],"will":[175],"significantly":[176],"outperform":[177],"other":[178],"algorithms":[179,196],"kernel.":[183],"Finally,":[184],"be":[187],"integrated":[188],"efficiently":[189],"existing":[191],"Multiple":[192],"Kernel":[193],"Learning":[194],"(MKL)":[195],"such":[197],"SimpleMKL.":[199]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}