{"id":"https://openalex.org/W2062946663","doi":"https://doi.org/10.1137/050646676","title":"A Symmetry Preserving Singular Value Decomposition","display_name":"A Symmetry Preserving Singular Value Decomposition","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2062946663","doi":"https://doi.org/10.1137/050646676","mag":"2062946663"},"language":"en","primary_location":{"id":"doi:10.1137/050646676","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646676","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080509063","display_name":"Mili Shah","orcid":"https://orcid.org/0000-0003-1789-6985"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mili I. Shah","raw_affiliation_strings":["**Rice University;"],"affiliations":[{"raw_affiliation_string":"**Rice University;","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109874470","display_name":"Danny C. Sorensen","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Danny C. Sorensen","raw_affiliation_strings":["**Rice University;"],"affiliations":[{"raw_affiliation_string":"**Rice University;","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080509063"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":null,"apc_paid":null,"fwci":5.1588,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.95805723,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"28","issue":"3","first_page":"749","last_page":"769"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9932000041007996,"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"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9932000041007996,"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/T10044","display_name":"Protein Structure and Dynamics","score":0.9810000061988831,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9800999760627747,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8410099744796753},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6320133805274963},{"id":"https://openalex.org/keywords/reflection-symmetry","display_name":"Reflection symmetry","score":0.6319195032119751},{"id":"https://openalex.org/keywords/plane-symmetry","display_name":"Plane symmetry","score":0.5666494965553284},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5652971267700195},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4932355284690857},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.46616584062576294},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.46269115805625916},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.35987037420272827},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.325552374124527},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3174422085285187},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18546569347381592},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1425786018371582}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8410099744796753},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6320133805274963},{"id":"https://openalex.org/C133978748","wikidata":"https://www.wikidata.org/wiki/Q15955882","display_name":"Reflection symmetry","level":2,"score":0.6319195032119751},{"id":"https://openalex.org/C40425006","wikidata":"https://www.wikidata.org/wiki/Q7201020","display_name":"Plane symmetry","level":2,"score":0.5666494965553284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5652971267700195},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4932355284690857},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.46616584062576294},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.46269115805625916},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.35987037420272827},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.325552374124527},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3174422085285187},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18546569347381592},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1425786018371582}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/050646676","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646676","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:CiteSeerX.psu:10.1.1.414.1548","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.414.1548","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.caam.rice.edu/caam/trs/2005/TR05-01.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.563.1397","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.563.1397","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.loyola.edu/~mili/SIMAX.pdf","raw_type":"text"},{"id":"pmh:oai:scholarship.rice.edu:1911/102033","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/102033","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical report"},{"id":"pmh:oai:scholarship.rice.edu:1911/102071","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/102071","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical report"},{"id":"pmh:oai:scholarship.rice.edu:1911/20648","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/20648","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W55767073","https://openalex.org/W619581422","https://openalex.org/W645620560","https://openalex.org/W1506690472","https://openalex.org/W1562445908","https://openalex.org/W1986145324","https://openalex.org/W2004026774","https://openalex.org/W2005358242","https://openalex.org/W2010464263","https://openalex.org/W2025923320","https://openalex.org/W2033894760","https://openalex.org/W2045598453","https://openalex.org/W2046060383","https://openalex.org/W2058897724","https://openalex.org/W2065705570","https://openalex.org/W2081231020","https://openalex.org/W2089884359","https://openalex.org/W2090238112","https://openalex.org/W2092590148","https://openalex.org/W2094954828","https://openalex.org/W2096573847","https://openalex.org/W2106763960","https://openalex.org/W2110121428","https://openalex.org/W2130259898","https://openalex.org/W2132589721","https://openalex.org/W2135463994","https://openalex.org/W2141299360","https://openalex.org/W2144634807","https://openalex.org/W2147824893","https://openalex.org/W2150302300","https://openalex.org/W2162737890","https://openalex.org/W2171314435","https://openalex.org/W2326953139","https://openalex.org/W3038698521"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W1607100495","https://openalex.org/W2147072251","https://openalex.org/W1990844505","https://openalex.org/W2148568324","https://openalex.org/W4386721910","https://openalex.org/W4378770618","https://openalex.org/W2164147222","https://openalex.org/W2038393145"],"abstract_inverted_index":{"A":[0],"reduced":[1,37],"order":[2],"representation":[3],"of":[4,24,31,82,90,115,121,124,128,156,167,175,178,181,187],"a":[5,13,19,32,109,125,133],"large":[6,126],"data":[7,158],"set":[8,127,145],"is":[9,51,61,170,190,197],"often":[10],"realized":[11],"through":[12],"principal":[14],"component":[15],"analysis":[16,45],"based":[17],"upon":[18],"singular":[20,29,136],"value":[21,137],"decomposition":[22,138],"(SVD)":[23],"the":[25,36,54,87,91,98,113,119,143,148,154,168,176,179,185,216],"data.":[26,55],"The":[27],"left":[28],"vectors":[30],"truncated":[33],"SVD":[34,79,99],"provide":[35,78],"basis.":[38],"In":[39,69,93],"several":[40],"applications":[41],"such":[42],"as":[43],"facial":[44],"and":[46,202],"protein":[47,70],"dynamics,":[48,71],"structural":[49],"symmetry":[50,60,74,96,117,123,134,183,189],"inherent":[52],"in":[53,66,97,153,160,200,208],"Typically,":[56],"reflective":[57,116,188],"or":[58,118,159,184],"rotational":[59,122,182],"expected":[62],"to":[63,77,111,204],"be":[64,205],"present":[65,108],"these":[67],"applications.":[68],"determining":[72],"this":[73],"allows":[75,100],"one":[76],"major":[80],"modes":[81],"motion":[83],"that":[84,140,212],"best":[85,141],"describe":[86],"symmetric":[88],"movements":[89],"protein.":[92],"face":[94],"detection,":[95],"for":[101],"more":[102],"efficient":[103],"compression":[104],"algorithms.":[105],"Here":[106],"we":[107,131],"method":[110],"compute":[112],"plane":[114,186],"axis":[120,180],"points.":[129],"Moreover,":[130],"develop":[132],"preserving":[135],"(SPSVD)":[139],"approximates":[142],"given":[144],"while":[146],"respecting":[147],"symmetry.":[149],"Interesting":[150],"subproblems":[151],"arise":[152],"presence":[155],"noisy":[157],"situations":[161],"where":[162],"most,":[163],"but":[164],"not":[165,214],"all,":[166],"structure":[169],"symmetric.":[171],"An":[172],"important":[173],"part":[174],"determination":[177],"an":[191],"iterative":[192],"reweighting":[193],"scheme.":[194],"This":[195],"scheme":[196],"rapidly":[198],"convergent":[199],"practice":[201],"seems":[203],"very":[206],"effective":[207],"ignoring":[209],"outliers":[210],"(points":[211],"do":[213],"respect":[215],"symmetry).":[217]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}