{"id":"https://openalex.org/W2916319383","doi":"https://doi.org/10.1137/20m1319577","title":"Matrix Denoising for Weighted Loss Functions and Heterogeneous Signals","display_name":"Matrix Denoising for Weighted Loss Functions and Heterogeneous Signals","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2916319383","doi":"https://doi.org/10.1137/20m1319577","mag":"2916319383"},"language":"en","primary_location":{"id":"doi:10.1137/20m1319577","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1319577","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/20M1319577","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/20M1319577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039324428","display_name":"William Leeb","orcid":"https://orcid.org/0000-0002-8617-3548"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"William E. Leeb","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8617-3548","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039324428"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7123,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.63372866,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"3","issue":"3","first_page":"987","last_page":"1012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9980999827384949,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9975000023841858,"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/noise-reduction","display_name":"Noise reduction","score":0.6431585550308228},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.6154574155807495},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5913918614387512},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5486035943031311},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5392948389053345},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4659487009048462},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46275684237480164},{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"Heteroscedasticity","score":0.4610442817211151},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4582800269126892},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4565228819847107},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45536747574806213},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21010065078735352},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15273278951644897}],"concepts":[{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.6431585550308228},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.6154574155807495},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5913918614387512},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5486035943031311},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5392948389053345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4659487009048462},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46275684237480164},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.4610442817211151},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4582800269126892},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4565228819847107},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45536747574806213},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21010065078735352},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15273278951644897},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1319577","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1319577","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/20M1319577","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1902.09474","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.09474","pdf_url":"https://arxiv.org/pdf/1902.09474","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2916319383","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1902.09474","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1902.09474","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1902.09474","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:10.1137/20m1319577","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1319577","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/20M1319577","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2300205785","display_name":null,"funder_award_id":"2018230","funder_id":"https://openalex.org/F4320308960","funder_display_name":"United States - Israel Binational Science Foundation"},{"id":"https://openalex.org/G8327040736","display_name":null,"funder_award_id":"IIS 1837992","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308960","display_name":"United States - Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2916319383.pdf","grobid_xml":"https://content.openalex.org/works/W2916319383.grobid-xml"},"referenced_works_count":70,"referenced_works":["https://openalex.org/W93530381","https://openalex.org/W1520752838","https://openalex.org/W1561774098","https://openalex.org/W1586554030","https://openalex.org/W1863732927","https://openalex.org/W1901790663","https://openalex.org/W1992442826","https://openalex.org/W1998635907","https://openalex.org/W2008054949","https://openalex.org/W2017304912","https://openalex.org/W2027515467","https://openalex.org/W2032291279","https://openalex.org/W2045547832","https://openalex.org/W2047071281","https://openalex.org/W2068832491","https://openalex.org/W2072864444","https://openalex.org/W2073169465","https://openalex.org/W2081940622","https://openalex.org/W2095534914","https://openalex.org/W2096192437","https://openalex.org/W2099079147","https://openalex.org/W2103437658","https://openalex.org/W2106005123","https://openalex.org/W2106084579","https://openalex.org/W2107665951","https://openalex.org/W2112680395","https://openalex.org/W2120872934","https://openalex.org/W2123226256","https://openalex.org/W2126846422","https://openalex.org/W2132657058","https://openalex.org/W2134332047","https://openalex.org/W2144730813","https://openalex.org/W2146746928","https://openalex.org/W2159601979","https://openalex.org/W2162635298","https://openalex.org/W2165395308","https://openalex.org/W2285319343","https://openalex.org/W2296319761","https://openalex.org/W2409128519","https://openalex.org/W2555502666","https://openalex.org/W2586353914","https://openalex.org/W2611328865","https://openalex.org/W2734385411","https://openalex.org/W2893930109","https://openalex.org/W2895327687","https://openalex.org/W2898076323","https://openalex.org/W2898873098","https://openalex.org/W2900374875","https://openalex.org/W2921439360","https://openalex.org/W2951638683","https://openalex.org/W2962769133","https://openalex.org/W2962946304","https://openalex.org/W2963092731","https://openalex.org/W2963106396","https://openalex.org/W2963304184","https://openalex.org/W2963705450","https://openalex.org/W2963780177","https://openalex.org/W2963899107","https://openalex.org/W2964234832","https://openalex.org/W2965497096","https://openalex.org/W3007034419","https://openalex.org/W3014527631","https://openalex.org/W3027159386","https://openalex.org/W3098139351","https://openalex.org/W3098807808","https://openalex.org/W3099053901","https://openalex.org/W3099514962","https://openalex.org/W3101545114","https://openalex.org/W3103692684","https://openalex.org/W3195187607"],"related_works":["https://openalex.org/W2796080709","https://openalex.org/W2132657058","https://openalex.org/W2060581589","https://openalex.org/W3119896830","https://openalex.org/W2550154328","https://openalex.org/W3123927683","https://openalex.org/W3104030484","https://openalex.org/W91766854","https://openalex.org/W2952885232","https://openalex.org/W2912457996","https://openalex.org/W2150382423","https://openalex.org/W3168889651","https://openalex.org/W3035325670","https://openalex.org/W3036371038","https://openalex.org/W1562453744","https://openalex.org/W3003022452","https://openalex.org/W2891363964","https://openalex.org/W3012767629","https://openalex.org/W2470465566","https://openalex.org/W3016266139"],"abstract_inverted_index":{"We":[0,72],"consider":[1],"the":[2,19,25,101],"problem":[3],"of":[4,27,37],"estimating":[5],"a":[6,10,35,94],"low-rank":[7],"matrix":[8,103],"from":[9],"noisy":[11],"observed":[12],"matrix.":[13],"Previous":[14],"work":[15],"has":[16],"shown":[17],"that":[18,97],"optimal":[20,74,90],"method":[21],"depends":[22],"crucially":[23],"on":[24],"choice":[26],"loss":[28,39,61,80],"function.":[29],"In":[30],"this":[31],"paper,":[32],"we":[33,86],"use":[34,88],"family":[36],"weighted":[38,60,79],"functions,":[40],"which":[41],"arise":[42],"naturally":[43],"for":[44,77],"problems":[45],"such":[46],"as":[47],"submatrix":[48],"denoising,":[49],"denoising":[50,55],"with":[51,56,107],"heteroscedastic":[52],"noise,":[53],"and":[54],"missing":[57],"data.":[58],"However,":[59],"functions":[62],"are":[63,69],"challenging":[64],"to":[65,92,104],"analyze":[66],"because":[67],"they":[68],"not":[70],"orthogonally-invariant.":[71],"derive":[73],"spectral":[75],"denoisers":[76,91],"these":[78,89],"functions.":[81],"By":[82],"combining":[83],"different":[84],"weights,":[85],"then":[87],"construct":[93],"new":[95],"denoiser":[96],"exploits":[98],"heterogeneity":[99],"in":[100],"signal":[102],"boost":[105],"estimation":[106],"unweighted":[108],"loss.":[109]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}