{"id":"https://openalex.org/W2063417791","doi":"https://doi.org/10.1109/ssp.2014.6884648","title":"Invariance of the distributions of normalized Gram matrices","display_name":"Invariance of the distributions of normalized Gram matrices","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2063417791","doi":"https://doi.org/10.1109/ssp.2014.6884648","mag":"2063417791"},"language":"en","primary_location":{"id":"doi:10.1109/ssp.2014.6884648","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssp.2014.6884648","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE Workshop on Statistical Signal Processing (SSP)","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":null,"display_name":"Stephen D. Howard","orcid":null},"institutions":[{"id":"https://openalex.org/I1303474014","display_name":"Defence Science and Technology Group","ror":"https://ror.org/05ddrvt52","country_code":"AU","type":"government","lineage":["https://openalex.org/I1303474014","https://openalex.org/I2801453606","https://openalex.org/I3139952251"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Stephen D. Howard","raw_affiliation_strings":["Defence Science and Technology Organisation, Edinburgh, Australia","Defence Sci. & Technol. Organ, Edinburgh, SA, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Defence Science and Technology Organisation, Edinburgh, Australia","institution_ids":["https://openalex.org/I1303474014"]},{"raw_affiliation_string":"Defence Sci. & Technol. Organ, Edinburgh, SA, Australia","institution_ids":["https://openalex.org/I1303474014"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089816970","display_name":"Songsri Sirianunpiboon","orcid":"https://orcid.org/0000-0001-5479-2435"},"institutions":[{"id":"https://openalex.org/I1303474014","display_name":"Defence Science and Technology Group","ror":"https://ror.org/05ddrvt52","country_code":"AU","type":"government","lineage":["https://openalex.org/I1303474014","https://openalex.org/I2801453606","https://openalex.org/I3139952251"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Songsri Sirianunpiboon","raw_affiliation_strings":["Defence Science and Technology Organisation, Edinburgh, Australia","Defence Sci. & Technol. Organ, Edinburgh, SA, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Defence Science and Technology Organisation, Edinburgh, Australia","institution_ids":["https://openalex.org/I1303474014"]},{"raw_affiliation_string":"Defence Sci. & Technol. Organ, Edinburgh, SA, Australia","institution_ids":["https://openalex.org/I1303474014"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112661161","display_name":"Douglas Cochran","orcid":null},"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":"Douglas Cochran","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA","IAFSE-ECEE: Sensor, Signal and Information Processing Center (SenSIP)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"IAFSE-ECEE: Sensor, Signal and Information Processing Center (SenSIP)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3799,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80723944,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"352","last_page":"355"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6398422122001648},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5012173652648926},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4761645495891571},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4743082523345947},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.45976346731185913},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.44229137897491455},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4276933968067169},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39848530292510986},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3913632333278656},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.372978150844574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.309897780418396},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2385687530040741},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18219393491744995},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.174424946308136},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15635555982589722}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6398422122001648},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5012173652648926},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4761645495891571},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4743082523345947},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.45976346731185913},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.44229137897491455},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4276933968067169},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39848530292510986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3913632333278656},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.372978150844574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.309897780418396},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2385687530040741},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18219393491744995},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.174424946308136},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15635555982589722},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ssp.2014.6884648","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssp.2014.6884648","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE Workshop on Statistical Signal Processing (SSP)","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":13,"referenced_works":["https://openalex.org/W1863655787","https://openalex.org/W1988358357","https://openalex.org/W2002539627","https://openalex.org/W2005886508","https://openalex.org/W2006366481","https://openalex.org/W2009188663","https://openalex.org/W2011069089","https://openalex.org/W2101478599","https://openalex.org/W2124342766","https://openalex.org/W2125391037","https://openalex.org/W2154477043","https://openalex.org/W2159582847","https://openalex.org/W2162597798"],"related_works":["https://openalex.org/W2062626603","https://openalex.org/W2165749285","https://openalex.org/W2009454197","https://openalex.org/W2474979212","https://openalex.org/W2562455930","https://openalex.org/W2001036795","https://openalex.org/W3093811938","https://openalex.org/W4390092784","https://openalex.org/W127450631","https://openalex.org/W2154748900"],"abstract_inverted_index":{"Normalized":[0],"Gram":[1,105],"matrices":[2,17,40],"formed":[3],"from":[4],"multiple":[5],"vectors":[6],"of":[7,12,15,35,38,48,53,82,85,102,113,134],"sensor":[8,61],"data,":[9],"and":[10,31,51,65],"functions":[11,34],"the":[13,36,57,60,83,86,100,111,114,122],"eigenvalues":[14,37,87],"such":[16],"in":[18,24,45,94],"particular,":[19],"have":[20],"a":[21,46,103],"long":[22],"history":[23],"connection":[25],"with":[26],"multiple-channel":[27],"detection.":[28],"The":[29,130],"determinant":[30,115],"various":[32],"other":[33],"these":[39,140],"arise":[41],"as":[42,108,116,118],"detection":[43],"statistics":[44],"variety":[47],"multichannel":[49],"problems,":[50],"knowledge":[52],"their":[54],"distributions":[55],"under":[56],"H0assumption":[58],"that":[59,124],"channels":[62],"are":[63],"independent":[64],"contain":[66],"only":[67],"white":[68,135],"gaussian":[69,136],"noise":[70,137],"is":[71,92,143],"consequently":[72],"important":[73],"for":[74,78,121],"determining":[75],"false-alarm":[76],"probabilities":[77],"multi-channel":[79],"detectors.":[80],"Invariance":[81],"H0distribution":[84,101],"to":[88,127],"one":[89],"data":[90],"channel":[91],"significant":[93],"some":[95],"applications.":[96],"This":[97],"paper":[98],"derives":[99],"normalized":[104],"matrix":[106,123],"and,":[107],"corollaries,":[109],"obtains":[110],"distribution":[112],"well":[117],"invariance":[119],"results":[120,141],"carry":[125],"over":[126],"its":[128],"spectrum.":[129],"essential":[131],"symmetry":[132],"property":[133],"on":[138],"which":[139],"depend":[142],"also":[144],"noted.":[145]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
