{"id":"https://openalex.org/W2163993511","doi":"https://doi.org/10.1109/iscas.2008.4541674","title":"Geometric structure of sum-of-rank-1 decompositions for n-dimensional order-p symmetric tensors","display_name":"Geometric structure of sum-of-rank-1 decompositions for n-dimensional order-p symmetric tensors","publication_year":2008,"publication_date":"2008-05-01","ids":{"openalex":"https://openalex.org/W2163993511","doi":"https://doi.org/10.1109/iscas.2008.4541674","mag":"2163993511"},"language":"en","primary_location":{"id":"doi:10.1109/iscas.2008.4541674","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2008.4541674","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Symposium on Circuits and Systems (ISCAS)","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/A5029977659","display_name":"Olexiy Kyrgyzov","orcid":null},"institutions":[{"id":"https://openalex.org/I165690674","display_name":"Oregon Health & Science University","ror":"https://ror.org/009avj582","country_code":"US","type":"education","lineage":["https://openalex.org/I165690674"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Olexiy Kyrgyzov","raw_affiliation_strings":["Department of Computer Science & Electrical Engineering, Oregon Health and Science University, Portland, USA","Department of Computer Science & Electrical Engineering, Oregon Health and Sciences University, Portland, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science & Electrical Engineering, Oregon Health and Science University, Portland, USA","institution_ids":["https://openalex.org/I165690674"]},{"raw_affiliation_string":"Department of Computer Science & Electrical Engineering, Oregon Health and Sciences University, Portland, USA","institution_ids":["https://openalex.org/I165690674"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083261801","display_name":"Deniz Erdo\u011fmu\u015f","orcid":"https://orcid.org/0000-0002-1114-3539"},"institutions":[{"id":"https://openalex.org/I165690674","display_name":"Oregon Health & Science University","ror":"https://ror.org/009avj582","country_code":"US","type":"education","lineage":["https://openalex.org/I165690674"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deniz Erdogmus","raw_affiliation_strings":["Department of Computer Science & Electrical Engineering, Oregon Health and Science University, Portland, USA","Department of Computer Science Electrical Engineering, Oregon Health and Sciences University, Portland, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science & Electrical Engineering, Oregon Health and Science University, Portland, USA","institution_ids":["https://openalex.org/I165690674"]},{"raw_affiliation_string":"Department of Computer Science Electrical Engineering, Oregon Health and Sciences University, Portland, USA","institution_ids":["https://openalex.org/I165690674"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029977659"],"corresponding_institution_ids":["https://openalex.org/I165690674"],"apc_list":null,"apc_paid":null,"fwci":0.471,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70967742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":null,"first_page":"1340","last_page":"1343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9376000165939331,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.916100025177002,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.6558594703674316},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6395137906074524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6391357779502869},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6110068559646606},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6018006205558777},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.4900261163711548},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4631608724594116},{"id":"https://openalex.org/keywords/rotation-formalisms-in-three-dimensions","display_name":"Rotation formalisms in three dimensions","score":0.4283480644226074},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4274812340736389},{"id":"https://openalex.org/keywords/invariants-of-tensors","display_name":"Invariants of tensors","score":0.4124518036842346},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37203365564346313},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3553251624107361},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3238813281059265},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2113279402256012},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19066089391708374}],"concepts":[{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.6558594703674316},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6395137906074524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6391357779502869},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6110068559646606},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6018006205558777},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.4900261163711548},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4631608724594116},{"id":"https://openalex.org/C171018156","wikidata":"https://www.wikidata.org/wiki/Q7370306","display_name":"Rotation formalisms in three dimensions","level":2,"score":0.4283480644226074},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4274812340736389},{"id":"https://openalex.org/C158158286","wikidata":"https://www.wikidata.org/wiki/Q9009080","display_name":"Invariants of tensors","level":3,"score":0.4124518036842346},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37203365564346313},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3553251624107361},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3238813281059265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2113279402256012},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19066089391708374},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"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/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iscas.2008.4541674","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2008.4541674","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Symposium on Circuits and Systems (ISCAS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1963826206","https://openalex.org/W1986326495","https://openalex.org/W2000215628","https://openalex.org/W2003787220","https://openalex.org/W2013912476","https://openalex.org/W2018282388","https://openalex.org/W2037271374","https://openalex.org/W2063708412","https://openalex.org/W2121739212","https://openalex.org/W2132267493","https://openalex.org/W2951139213"],"related_works":["https://openalex.org/W2766953420","https://openalex.org/W2951776006","https://openalex.org/W2703906751","https://openalex.org/W2945020546","https://openalex.org/W3213289256","https://openalex.org/W3198635941","https://openalex.org/W3214531188","https://openalex.org/W2005375943","https://openalex.org/W2738262030","https://openalex.org/W4353081986"],"abstract_inverted_index":{"The":[0,119],"canonical":[1],"sum-of-rank-one":[2,116],"decomposition":[3,38,152],"of":[4,36,46,64,68,79,103,121,136,141,144,151,161],"tensors":[5,123],"is":[6,61],"a":[7,84,101,128,162],"fundamental":[8],"linear":[9,58],"algebraic":[10],"problem":[11],"encountered":[12],"in":[13],"signal":[14],"processing,":[15],"machine":[16],"learning,":[17],"and":[18,95,149],"other":[19],"scientific":[20],"fields.":[21],"Current":[22],"algorithms":[23],"that":[24,39,48,105],"emerge":[25],"from":[26],"CANDECOMP":[27],"or":[28],"PARAFAC":[29],"formalisms":[30],"rely":[31],"on":[32,87],"the":[33,43,53,65,76,88,93,97,131,145,159],"basic":[34],"definition":[35],"tensor":[37,54,113],"describes":[40],"rank":[41],"as":[42,83],"minimum":[44],"number":[45],"vectors":[47],"are":[49,124,138,165],"needed":[50],"to":[51,109,126],"reconstruct":[52],"using":[55,155],"outer":[56],"product":[57],"combinations,":[59],"which":[60],"an":[62],"extension":[63],"same":[66],"property":[67],"matrix":[69,81],"rank.":[70],"In":[71],"this":[72],"paper,":[73],"we":[74,99],"reinterpret":[75],"orthogonality":[77],"condition":[78],"symmetric":[80,112],"eigenvectors":[82,94,120,137],"geometric":[85,147],"constraint":[86],"coordinate":[89],"frame":[90,129],"formed":[91],"by":[92],"relaxing":[96],"orthogonality,":[98],"develop":[100],"set":[102],"structured-bases":[104],"can":[106],"be":[107],"utilized":[108],"decompose":[110],"any":[111],"into":[114],"its":[115],"(canonical)":[117],"decomposition.":[118],"order-p":[122],"observed":[125],"form":[127],"where":[130],"angle":[132],"between":[133],"various":[134],"pairs":[135],"integer":[139],"multiples":[140],"pi/p.":[142],"Validation":[143],"proposed":[146],"structure":[148],"demonstration":[150],"accuracies":[153],"obtained":[154],"these":[156],"frames":[157],"(at":[158],"level":[160],"computer's":[163],"numerical-epsiv)":[164],"provided.":[166]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}