{"id":"https://openalex.org/W4416057942","doi":"https://doi.org/10.1109/isbi61048.2026.11515661","title":"SO(3)-Invariant PCA with Application to Molecular Data","display_name":"SO(3)-Invariant PCA with Application to Molecular Data","publication_year":2026,"publication_date":"2026-04-08","ids":{"openalex":"https://openalex.org/W4416057942","doi":"https://doi.org/10.1109/isbi61048.2026.11515661"},"language":null,"primary_location":{"id":"doi:10.1109/isbi61048.2026.11515661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isbi61048.2026.11515661","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2026 IEEE 23rd International Symposium on Biomedical Imaging (ISBI)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.18827","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120320933","display_name":"Michael Fraiman","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Michael Fraiman","raw_affiliation_strings":["School of Mathematical Sciences, Tel Aviv University,Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University,Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037588036","display_name":"Paulina Hoyos","orcid":"https://orcid.org/0009-0009-8949-998X"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paulina Hoyos","raw_affiliation_strings":["UT Austin,Department of Mathematics,USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UT Austin,Department of Mathematics,USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109581449","display_name":"Tamir Bendory","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Tamir Bendory","raw_affiliation_strings":["School of Electrical and Computer Engineering, Tel Aviv University,Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Tel Aviv University,Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035113400","display_name":"Joe Kileel","orcid":"https://orcid.org/0000-0001-9926-9170"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joe Kileel","raw_affiliation_strings":["UT Austin,Department of Mathematics,USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UT Austin,Department of Mathematics,USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040080749","display_name":"Oscar Mickelin","orcid":"https://orcid.org/0000-0003-0167-1992"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Oscar Mickelin","raw_affiliation_strings":["Yau Mathematical Sciences Center, Tsinghua University,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yau Mathematical Sciences Center, Tsinghua University,China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035215153","display_name":"Nir Sharon","orcid":"https://orcid.org/0000-0001-6329-3857"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Nir Sharon","raw_affiliation_strings":["School of Mathematical Sciences, Tel Aviv University,Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University,Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062844820","display_name":"Amit Singer","orcid":"https://orcid.org/0000-0002-6975-7955"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Amit Singer","raw_affiliation_strings":["Princeton University,Program in Applied and Computational Mathematics,Department of Mathematics,USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University,Program in Applied and Computational Mathematics,Department of Mathematics,USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5120320933"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00153653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10044","display_name":"Protein Structure and Dynamics","score":0.3391000032424927,"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/T10044","display_name":"Protein Structure and Dynamics","score":0.3391000032424927,"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/T12303","display_name":"Tensor decomposition and applications","score":0.08900000154972076,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.04390000179409981,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.8281999826431274},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.734000027179718},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6033999919891357},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5414999723434448},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5378000140190125},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5267000198364258},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4823000133037567},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.41290000081062317}],"concepts":[{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.8281999826431274},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.734000027179718},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6033999919891357},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5666999816894531},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5414999723434448},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5378000140190125},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5267000198364258},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48660001158714294},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4406999945640564},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.41290000081062317},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4027000069618225},{"id":"https://openalex.org/C153914771","wikidata":"https://www.wikidata.org/wiki/Q5227343","display_name":"Data reduction","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3880999982357025},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C2780977526","wikidata":"https://www.wikidata.org/wiki/Q42417149","display_name":"Data exploration","level":3,"score":0.32260000705718994},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.27399998903274536}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/isbi61048.2026.11515661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isbi61048.2026.11515661","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2026 IEEE 23rd International Symposium on Biomedical Imaging (ISBI)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2510.18827","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.18827","pdf_url":"https://arxiv.org/pdf/2510.18827","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2510.18827","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.18827","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":"pmh:oai:arXiv.org:2510.18827","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.18827","pdf_url":"https://arxiv.org/pdf/2510.18827","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[{"id":"https://openalex.org/G246103337","display_name":null,"funder_award_id":"514588180","funder_id":"https://openalex.org/F4320308022","funder_display_name":"California Department of Fish and Game"},{"id":"https://openalex.org/G2572851558","display_name":null,"funder_award_id":"2020159,2024266","funder_id":"https://openalex.org/F4320306259","funder_display_name":"Bonfils-Stanton Foundation"},{"id":"https://openalex.org/G5213515250","display_name":null,"funder_award_id":"CISE-IIS 2312746,DE SC0025312","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6282933724","display_name":null,"funder_award_id":"FA9550-23-1-0249","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6908146112","display_name":null,"funder_award_id":"1924/21","funder_id":"https://openalex.org/F4320313643","funder_display_name":"Iowa Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320306259","display_name":"Bonfils-Stanton Foundation","ror":"https://ror.org/03n0et212"},{"id":"https://openalex.org/F4320308022","display_name":"California Department of Fish and Game","ror":"https://ror.org/02v6w2r95"},{"id":"https://openalex.org/F4320313643","display_name":"Iowa Science Foundation","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Principal":[0],"component":[1],"analysis":[2],"(PCA)":[3],"is":[4],"a":[5,102],"fundamental":[6],"technique":[7],"for":[8,65,71,123],"dimensionality":[9],"reduction":[10,104],"and":[11,62,118],"denoising;":[12],"however,":[13],"its":[14,116],"application":[15],"to":[16,51],"three-dimensional":[17],"data":[18,76],"with":[19,34,55],"arbitrary":[20],"orientations\u2014common":[21],"in":[22,101,105],"structural":[23],"biology\u2014presents":[24],"significant":[25],"challenges.":[26],"A":[27],"naive":[28],"approach":[29],"requires":[30],"augmenting":[31],"the":[32,86,90,94,109],"dataset":[33],"many":[35],"rotated":[36],"copies":[37],"of":[38,93,97],"each":[39],"sample,":[40],"incurring":[41],"prohibitive":[42],"computational":[43],"costs.":[44],"In":[45],"this":[46],"paper,":[47],"we":[48,83],"extend":[49],"PCA":[50,67],"3D":[52],"volumetric":[53],"datasets":[54],"unknown":[56],"orientations":[57],"by":[58],"developing":[59],"an":[60],"efficient":[61],"principled":[63],"framework":[64],"SO(3)-invariant":[66],"that":[68,85],"implicitly":[69],"accounts":[70],"all":[72],"rotations":[73],"without":[74],"explicit":[75],"augmentation.":[77],"By":[78],"exploiting":[79],"underlying":[80],"algebraic":[81],"structure,":[82],"demonstrate":[84],"computation":[87],"involves":[88],"only":[89],"square":[91],"root":[92],"total":[95],"number":[96],"covariance":[98],"entries,":[99],"resulting":[100],"substantial":[103],"complexity.":[106],"We":[107],"validate":[108],"method":[110],"on":[111],"real-world":[112],"molecular":[113],"datasets,":[114],"demonstrating":[115],"effectiveness":[117],"opening":[119],"up":[120],"new":[121],"possibilities":[122],"large-scale,":[124],"high-dimensional":[125],"reconstruction":[126],"problems.":[127]},"counts_by_year":[],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-24T00:00:00"}