{"id":"https://openalex.org/W7161937003","doi":"https://doi.org/10.48550/arxiv.2605.20681","title":"Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis","display_name":"Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis","publication_year":2026,"publication_date":"2026-05-20","ids":{"openalex":"https://openalex.org/W7161937003","doi":"https://doi.org/10.48550/arxiv.2605.20681"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.20681","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20681","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.20681","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136628987","display_name":"Kisung You","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"You, Kisung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5136628987"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.6026999950408936,"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"}},"topics":[{"id":"https://openalex.org/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.6026999950408936,"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/T10136","display_name":"Statistical Methods and Inference","score":0.10100000351667404,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.03779999911785126,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/principal-component-analysis","display_name":"Principal component analysis","score":0.7197999954223633},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.6863999962806702},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.616599977016449},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.590399980545044},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5734999775886536},{"id":"https://openalex.org/keywords/calibration","display_name":"Calibration","score":0.45809999108314514},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.44429999589920044},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4381999969482422},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.4226999878883362}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7627000212669373},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.7197999954223633},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6863999962806702},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.616599977016449},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.590399980545044},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5734999775886536},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47530001401901245},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.45809999108314514},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4381999969482422},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.4226999878883362},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39730000495910645},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3831000030040741},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C67226441","wikidata":"https://www.wikidata.org/wiki/Q1665389","display_name":"Robust statistics","level":3,"score":0.3668999969959259},{"id":"https://openalex.org/C2777749129","wikidata":"https://www.wikidata.org/wiki/Q17148469","display_name":"Robust principal component analysis","level":3,"score":0.35850000381469727},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3513999879360199},{"id":"https://openalex.org/C71176878","wikidata":"https://www.wikidata.org/wiki/Q17014987","display_name":"Functional principal component analysis","level":3,"score":0.335099995136261},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.33239999413490295},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C136368487","wikidata":"https://www.wikidata.org/wiki/Q7979899","display_name":"Weighted median","level":5,"score":0.32409998774528503},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C116714509","wikidata":"https://www.wikidata.org/wiki/Q32278","display_name":"Truncated mean","level":3,"score":0.29840001463890076},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.272599995136261},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C180623205","wikidata":"https://www.wikidata.org/wiki/Q1268589","display_name":"Outer product","level":3,"score":0.2590999901294708},{"id":"https://openalex.org/C74887250","wikidata":"https://www.wikidata.org/wiki/Q3455892","display_name":"Principal component regression","level":3,"score":0.258899986743927},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.20681","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20681","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.20681","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.20681","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Distributed":[0],"principal":[1,15],"component":[2,60,69],"analysis":[3],"(PCA)":[4],"produces":[5],"node-level":[6,53],"estimates":[7],"of":[8,45,95],"both":[9],"a":[10,14,23,34,77,91,153],"mean":[11,27,59],"vector":[12],"and":[13,29,48,110,120,132,137,151],"subspace.":[16],"Robustly":[17],"aggregating":[18],"these":[19],"heterogeneous":[20],"objects":[21],"requires":[22],"relative":[24],"scale":[25,144],"between":[26],"error":[28],"subspace":[30,68,149],"error.":[31],"We":[32,75,116],"study":[33],"scale-calibrated":[35],"median-of-means":[36,85,126],"estimator":[37,86],"for":[38],"this":[39],"problem":[40],"using":[41],"the":[42,49,58,62,67,82],"product":[43],"geometry":[44],"Euclidean":[46],"space":[47],"Grassmann":[50],"manifold.":[51],"A":[52],"PCA":[54,156],"expansion":[55],"shows":[56],"that":[57,81,143],"has":[61],"usual":[63],"linear":[64],"influence,":[65,131],"whereas":[66],"is":[70,87],"an":[71,111],"eigengap-weighted":[72],"covariance":[73,114],"perturbation.":[74],"prove":[76,133],"local":[78],"reduction":[79],"showing":[80],"proposed":[83],"product-manifold":[84],"asymptotically":[88],"equivalent":[89],"to":[90,147],"scaled":[92],"spatial":[93],"median":[94],"node":[96],"influence":[97],"errors.":[98],"This":[99],"yields":[100],"fixed-node":[101],"non-Gaussian":[102],"limits,":[103],"growing-node":[104],"Gaussian":[105],"limits":[106],"with":[107],"finite-block":[108],"bias,":[109],"explicit":[112],"scale-dependent":[113],"formula.":[115],"propose":[117],"robust":[118,154],"block-scale":[119],"inference-optimal":[121],"calibration":[122,145],"rules,":[123],"establish":[124],"high-probability":[125],"bounds,":[127],"characterize":[128],"factorwise":[129],"bad-node":[130],"node-bootstrap":[134],"validity.":[135],"Simulations":[136],"large-scale":[138],"single-cell":[139],"RNA-seq":[140],"data":[141],"show":[142],"adapts":[146],"eigengap-driven":[148],"uncertainty":[150],"provides":[152],"distributed":[155],"summary.":[157]},"counts_by_year":[],"updated_date":"2026-05-22T06:22:51.596421","created_date":"2026-05-22T00:00:00"}