{"id":"https://openalex.org/W7214652299","doi":"https://doi.org/10.48550/arxiv.2609.30720","title":"Optimal Personalized Subspace Learning for Multi-view Tensor Observations","display_name":"Optimal Personalized Subspace Learning for Multi-view Tensor Observations","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214652299","doi":"https://doi.org/10.48550/arxiv.2609.30720"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30720","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30720","pdf_url":"https://arxiv.org/pdf/2609.30720","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.30720","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134324130","display_name":"Kangxiang Qin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qin, Kangxiang","raw_affiliation_strings":["Institute for Financial Studies Shandong University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Financial Studies Shandong University","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153195342","display_name":"Zeyu Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Zeyu","raw_affiliation_strings":["Institute for Financial Studies Shandong University","School of Statistics and Data Science Southeast University Xinbing Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Financial Studies Shandong University","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"School of Statistics and Data Science Southeast University Xinbing Kong","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121896421","display_name":"Xinbing Kong","orcid":"https://orcid.org/0000-0002-6521-6000","observed_orcids":["https://orcid.org/0000-0002-6521-6000"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kong, Xinbing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103389037","display_name":"Wang Zhou","orcid":"https://orcid.org/0000-0002-1970-0096","observed_orcids":["https://orcid.org/0000-0002-1970-0096","https://orcid.org/0000-0003-4413-4441"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I4210090971","display_name":"Southeast University","ror":"https://ror.org/00cf0ab87","country_code":"BD","type":"education","lineage":["https://openalex.org/I4210090971"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["BD","CN","SG"],"is_corresponding":false,"raw_author_name":"Zhou, Wang","raw_affiliation_strings":["Department of Statistics and Applied Probability National University of Singapore","School of Statistics and Data Science Southeast University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Applied Probability National University of Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"School of Statistics and Data Science Southeast University","institution_ids":["https://openalex.org/I4210090971","https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9990000128746033,"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":0.9990000128746033,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":9.999999747378752e-05,"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/T10057","display_name":"Face and Expression Recognition","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tucker-decomposition","display_name":"Tucker decomposition","score":0.8489999771118164},{"id":"https://openalex.org/keywords/minimax-lower-bounds","display_name":"minimax lower bounds","score":0.8659999966621399},{"id":"https://openalex.org/keywords/closed-form-estimation","display_name":"closed-form estimation","score":0.6420000195503235},{"id":"https://openalex.org/keywords/tensor-principal-component-analysis","display_name":"tensor principal component analysis","score":0.47999998927116394},{"id":"https://openalex.org/keywords/power-management","display_name":"power management","score":0.7860000133514404},{"id":"https://openalex.org/keywords/financial-analysis","display_name":"financial analysis","score":0.9160000085830688},{"id":"https://openalex.org/keywords/activity-recognition","display_name":"activity recognition","score":1.0}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.8202000260353088},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7537000179290771},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.6888999938964844},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5989999771118164},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.546999990940094},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5185999870300293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5117999911308289},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.4966999888420105},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48750001192092896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47600001096725464},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4697999954223633},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.45579999685287476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40400001406669617},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3635999858379364},{"id":"https://openalex.org/C51432778","wikidata":"https://www.wikidata.org/wiki/Q1259145","display_name":"Independent component analysis","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.32269999384880066},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C184297639","wikidata":"https://www.wikidata.org/wiki/Q177765","display_name":"Biometrics","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31299999356269836},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.28519999980926514},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C2777749129","wikidata":"https://www.wikidata.org/wiki/Q17148469","display_name":"Robust principal component analysis","level":3,"score":0.2671999931335449},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.26510000228881836},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2597000002861023},{"id":"https://openalex.org/C2780692498","wikidata":"https://www.wikidata.org/wiki/Q16950721","display_name":"Component analysis","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30720","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30720","pdf_url":"https://arxiv.org/pdf/2609.30720","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.30720","doi":"https://doi.org/10.48550/arxiv.2609.30720","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30720","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.30720","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30720","pdf_url":"https://arxiv.org/pdf/2609.30720","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214652299.pdf","grobid_xml":"https://content.openalex.org/works/W7214652299.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W2131172946","https://openalex.org/W2972410720","https://openalex.org/W3147394507","https://openalex.org/W4285213314","https://openalex.org/W4392780972","https://openalex.org/W4399597630","https://openalex.org/W4404986675","https://openalex.org/W4405253997","https://openalex.org/W4406548272","https://openalex.org/W4406890615","https://openalex.org/W4409419476","https://openalex.org/W4417065301","https://openalex.org/W7118160067","https://openalex.org/W7148290532"],"related_works":["https://openalex.org/W4383988829","https://openalex.org/W2921505325","https://openalex.org/W3016388692","https://openalex.org/W2893419682","https://openalex.org/W4360981195","https://openalex.org/W3007380221","https://openalex.org/W3143185276","https://openalex.org/W7163675506","https://openalex.org/W4406529876","https://openalex.org/W2945636478"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,49],"model":[4],"the":[5,11,21,33,44,84,94,99,110,130,144,148],"observed":[6],"multi-view":[7],"tensors":[8],"by":[9,87],"decomposing":[10],"underlying":[12],"signal":[13],"in":[14,103,151],"each":[15],"view":[16],"into":[17],"two":[18],"components:":[19],"(i)":[20],"shared":[22,45],"component":[23,35,57],"that":[24,36,93,128],"captures":[25],"common":[26],"dynamics":[27],"across":[28,121],"all":[29],"views,":[30,122],"and":[31,46,69,140,158],"(ii)":[32],"private":[34,47],"accounts":[37],"for":[38,61,75],"view-wise":[39,106],"unique":[40],"variations.":[41],"To":[42],"decouple":[43],"components,":[48],"introduce":[50],"a":[51,65,115],"novel":[52],"Tucker":[53],"personalized":[54,79],"subspace":[55],"principal":[56],"analysis":[58,91],"(TPS-PCA)":[59],"approach":[60],"tensors,":[62],"which":[63,123],"admits":[64],"one-step":[66],"closed-form":[67],"solution":[68],"serves":[70],"as":[71],"an":[72],"ideal":[73],"surrogate":[74],"our":[76],"extended":[77],"tensor-version":[78],"PCA":[80],"(TP-PCA),":[81],"adapted":[82],"from":[83],"seminal":[85],"work":[86],"\\cite{shi2024personalized}.":[88],"The":[89],"theoretical":[90],"reveals":[92],"proposed":[95,149],"TPS-PCA":[96,131],"estimators":[97,112],"reach":[98],"minimax":[100],"lower":[101],"bound":[102],"terms":[104],"of":[105,117,129,147],"tensor":[107],"decoupling,":[108],"whereas":[109],"TP-PCA":[111],"only":[113],"achieve":[114],"rate":[116],"average":[118],"decoupling":[119],"error":[120],"is":[124],"still":[125],"slower":[126],"than":[127],"estimators.":[132],"Extensive":[133],"numerical":[134],"experiments":[135],"are":[136],"conducted":[137],"on":[138],"synthetic":[139],"real":[141],"datasets,":[142],"demonstrating":[143],"wide":[145],"applicability":[146],"method":[150],"fields":[152],"including":[153],"power":[154],"management,":[155],"financial":[156],"analysis,":[157],"activity":[159],"recognition.":[160]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-29T00:00:00"}