{"id":"https://openalex.org/W2035062691","doi":"https://doi.org/10.1137/070692121","title":"A Method to Avoid Diverging Components in the Candecomp/Parafac Model for Generic $I\\timesJ\\times2$ Arrays","display_name":"A Method to Avoid Diverging Components in the Candecomp/Parafac Model for Generic $I\\timesJ\\times2$ Arrays","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2035062691","doi":"https://doi.org/10.1137/070692121","mag":"2035062691"},"language":"en","primary_location":{"id":"doi:10.1137/070692121","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070692121","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/12e102b0-ba85-4bc7-8fa4-540ab58353e2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084820167","display_name":"Alwin Stegeman","orcid":"https://orcid.org/0000-0003-3385-2560"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alwin Stegeman","raw_affiliation_strings":["a.w.stegeman@rug.nl and http://www.gmw.rug.nl/$\\\\sim$stegeman#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"a.w.stegeman@rug.nl and http://www.gmw.rug.nl/$\\\\sim$stegeman#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009006026","display_name":"Lieven De Lathauwer","orcid":"https://orcid.org/0000-0001-5562-5014"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Lieven De Lathauwer","raw_affiliation_strings":["lieven.delathauwer@kuleuven-kortrijk.be#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"lieven.delathauwer@kuleuven-kortrijk.be#TAB#","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.571,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.91479821,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"1614","last_page":"1638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9969000220298767,"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":0.9969000220298767,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.8427309989929199},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7970861196517944},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6558867692947388},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.654403567314148},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5755710005760193},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5655157566070557},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.483510285615921},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4426247477531433},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4244939982891083},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4170498251914978},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2901442050933838},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15471667051315308},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09280034899711609},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07657411694526672}],"concepts":[{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.8427309989929199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7970861196517944},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6558867692947388},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.654403567314148},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5755710005760193},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5655157566070557},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.483510285615921},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4426247477531433},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4244939982891083},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4170498251914978},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2901442050933838},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15471667051315308},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09280034899711609},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07657411694526672},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070692121","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070692121","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:pure.rug.nl:openaire/12e102b0-ba85-4bc7-8fa4-540ab58353e2","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/12e102b0-ba85-4bc7-8fa4-540ab58353e2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stegeman, A & De lathauwer, L 2008, 'A Method to Avoid Diverging Components in the Candecomp/Parafac Model for Generic I \u00d7 J \u00d7 2 Arrays', SIAM Journal on Matrix Analysis and Applications, vol. 30, no. 4, pp. 1614-1638. https://doi.org/10.1137/070692121","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/12e102b0-ba85-4bc7-8fa4-540ab58353e2","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/12e102b0-ba85-4bc7-8fa4-540ab58353e2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stegeman, A & De lathauwer, L 2008, 'A Method to Avoid Diverging Components in the Candecomp/Parafac Model for Generic I \u00d7 J \u00d7 2 Arrays', SIAM Journal on Matrix Analysis and Applications, vol. 30, no. 4, pp. 1614-1638. https://doi.org/10.1137/070692121","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W3392783","https://openalex.org/W158789882","https://openalex.org/W227277429","https://openalex.org/W1548802052","https://openalex.org/W1963826206","https://openalex.org/W1965965675","https://openalex.org/W1978137488","https://openalex.org/W1981745143","https://openalex.org/W2000045479","https://openalex.org/W2000215628","https://openalex.org/W2008560788","https://openalex.org/W2011179711","https://openalex.org/W2024166170","https://openalex.org/W2026698804","https://openalex.org/W2027559251","https://openalex.org/W2033154334","https://openalex.org/W2038028644","https://openalex.org/W2047680880","https://openalex.org/W2049722592","https://openalex.org/W2057503509","https://openalex.org/W2065931606","https://openalex.org/W2076603483","https://openalex.org/W2078291856","https://openalex.org/W2078789945","https://openalex.org/W2082658029","https://openalex.org/W2089079408","https://openalex.org/W2090963365","https://openalex.org/W2092978222","https://openalex.org/W2099741732","https://openalex.org/W2101641981","https://openalex.org/W2105186495","https://openalex.org/W2112451877","https://openalex.org/W2112702842","https://openalex.org/W2119741678","https://openalex.org/W2121739212","https://openalex.org/W2132220618","https://openalex.org/W2132267493","https://openalex.org/W2136023375","https://openalex.org/W2156982859","https://openalex.org/W2162440838","https://openalex.org/W2170668800","https://openalex.org/W2258054274","https://openalex.org/W2330159389","https://openalex.org/W2610857016","https://openalex.org/W2617854063","https://openalex.org/W2915098601"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W4234996786","https://openalex.org/W2025511434","https://openalex.org/W2963179930","https://openalex.org/W1989925552","https://openalex.org/W2061460135","https://openalex.org/W3102632868","https://openalex.org/W2050801211","https://openalex.org/W2783911801","https://openalex.org/W2952285051"],"abstract_inverted_index":{"Computing":[0],"the":[1,9,56,71,90,94],"Candecomp/Parafac":[2],"(CP)":[3],"solution":[4,88],"of":[5,58,64,76,93,96],"R":[6],"components":[7,34,103],"(i.e.,":[8],"best":[10,72],"rank-R":[11],"approximation)":[12],"for":[13],"a":[14,31,77,111,116,122,127],"generic":[15],"$I\\times":[16],"J\\times":[17],"2$":[18],"array":[19],"may":[20],"result":[21],"in":[22,38],"diverging":[23,102],"components,":[24],"also":[25],"known":[26],"as":[27],"\u201cdegeneracy.\u201d":[28],"In":[29],"such":[30],"case,":[32],"several":[33],"are":[35],"highly":[36],"correlated":[37],"all":[39],"three":[40],"modes,":[41],"and":[42,106,115,126,138],"their":[43],"component":[44],"weights":[45],"become":[46],"arbitrarily":[47],"large.":[48],"Evidence":[49],"exists":[50],"that":[51],"this":[52],"is":[53,89],"caused":[54],"by":[55,74],"nonexistence":[57],"an":[59],"optimal":[60],"CP":[61,97,113,124],"solution.":[62],"Instead":[63],"using":[65],"CP,":[66],"we":[67],"propose":[68],"to":[69,134],"compute":[70],"approximation":[73],"means":[75],"generalized":[78],"Schur":[79],"decomposition":[80],"(GSD),":[81],"which":[82],"always":[83],"exists.":[84],"The":[85],"obtained":[86],"GSD":[87,129],"limit":[91],"point":[92],"sequence":[95],"updates":[98],"(whether":[99],"it":[100],"features":[101],"or":[104,120],"not)":[105],"can":[107],"be":[108],"separated":[109],"into":[110,121],"nondiverging":[112,123],"part":[114,119,125],"sparse":[117],"Tucker3":[118],"smaller":[128],"part.":[130],"We":[131],"show":[132],"how":[133],"obtain":[135],"both":[136],"representations":[137],"illustrate":[139],"our":[140],"results":[141],"with":[142],"numerical":[143],"experiments.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}