{"id":"https://openalex.org/W3031547348","doi":"https://doi.org/10.1137/20m1342124","title":"Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise","display_name":"Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3031547348","doi":"https://doi.org/10.1137/20m1342124","mag":"3031547348","pmid":"https://pubmed.ncbi.nlm.nih.gov/34124607"},"language":"en","primary_location":{"id":"doi:10.1137/20m1342124","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1342124","pdf_url":null,"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","pubmed"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/20m1342124","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031605523","display_name":"Boris Landa","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Boris Landa","raw_affiliation_strings":["Program in Applied Mathematics, Yale University","Yale University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Program in Applied Mathematics, Yale University","institution_ids":["https://openalex.org/I4210131439","https://openalex.org/I32971472"]},{"raw_affiliation_string":"Yale University","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110436903","display_name":"Ronald R. Coifman","orcid":"https://orcid.org/0000-0001-7336-7784"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald R. Coifman","raw_affiliation_strings":["Program in Applied Mathematics, Yale University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Program in Applied Mathematics, Yale University","institution_ids":["https://openalex.org/I4210131439","https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020473435","display_name":"Yuval Kluger","orcid":"https://orcid.org/0000-0002-3035-071X"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuval Kluger","raw_affiliation_strings":["Department of Pathology, Yale University School of Medicine","Interdepartmental Program in Computational Biology and Bioinformatics, Yale University","Program in Applied Mathematics, Yale University","3 Department of Pathology, Yale University School of Medicine"],"raw_orcid":"https://orcid.org/0000-0002-3035-071X","affiliations":[{"raw_affiliation_string":"Department of Pathology, Yale University School of Medicine","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Interdepartmental Program in Computational Biology and Bioinformatics, Yale University","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Program in Applied Mathematics, Yale University","institution_ids":["https://openalex.org/I4210131439","https://openalex.org/I32971472"]},{"raw_affiliation_string":"3 Department of Pathology, Yale University School of Medicine","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031605523"],"corresponding_institution_ids":["https://openalex.org/I32971472","https://openalex.org/I4210131439"],"apc_list":null,"apc_paid":null,"fwci":0.0813,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.41501301,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":"1","first_page":"388","last_page":"413"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.9998000264167786,"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":0.9998000264167786,"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/T10885","display_name":"Gene expression and cancer classification","score":0.9972000122070312,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9961000084877014,"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/heteroscedasticity","display_name":"Heteroscedasticity","score":0.8660174608230591},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.7091548442840576},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.5816305875778198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5412132740020752},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5276234149932861},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4811031222343445},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4429612159729004},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4428153336048126},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30459731817245483},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24724739789962769},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18299901485443115},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14193546772003174}],"concepts":[{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.8660174608230591},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.7091548442840576},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.5816305875778198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5412132740020752},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5276234149932861},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4811031222343445},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4429612159729004},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4428153336048126},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30459731817245483},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24724739789962769},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18299901485443115},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14193546772003174},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","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},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/20m1342124","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1342124","pdf_url":null,"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":"pmid:34124607","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34124607","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"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":null},{"id":"pmh:oai:arXiv.org:2006.00402","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.00402","pdf_url":"https://arxiv.org/pdf/2006.00402","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":null,"raw_type":"text"},{"id":"mag:3031547348","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.00402","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":"pmh:oai:pubmedcentral.nih.gov:8194191","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8194191","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Math Data Sci","raw_type":"Text"},{"id":"doi:10.48550/arxiv.2006.00402","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.00402","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:10.1137/20m1342124","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1342124","pdf_url":null,"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/G160350609","display_name":null,"funder_award_id":"5R01NS10004903","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G233314128","display_name":null,"funder_award_id":"2P50CA121974","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G6053781650","display_name":null,"funder_award_id":"R01GM131642","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G7742415388","display_name":null,"funder_award_id":"R01HG008383","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"}],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W1566036427","https://openalex.org/W1579743691","https://openalex.org/W1779908107","https://openalex.org/W1963766113","https://openalex.org/W1980494867","https://openalex.org/W1981466805","https://openalex.org/W1984032850","https://openalex.org/W2003447360","https://openalex.org/W2007153785","https://openalex.org/W2018612061","https://openalex.org/W2079639858","https://openalex.org/W2094700196","https://openalex.org/W2097073572","https://openalex.org/W2097308346","https://openalex.org/W2101491865","https://openalex.org/W2102212449","https://openalex.org/W2103012681","https://openalex.org/W2103829273","https://openalex.org/W2117684310","https://openalex.org/W2119227770","https://openalex.org/W2121947440","https://openalex.org/W2127048411","https://openalex.org/W2130158951","https://openalex.org/W2132914434","https://openalex.org/W2141599824","https://openalex.org/W2141695289","https://openalex.org/W2141999998","https://openalex.org/W2149573463","https://openalex.org/W2152322845","https://openalex.org/W2158131535","https://openalex.org/W2158787690","https://openalex.org/W2161997479","https://openalex.org/W2165874743","https://openalex.org/W2187089797","https://openalex.org/W2230899220","https://openalex.org/W2332292689","https://openalex.org/W2486882743","https://openalex.org/W2522454188","https://openalex.org/W2558748708","https://openalex.org/W2568381517","https://openalex.org/W2571662414","https://openalex.org/W2605810679","https://openalex.org/W2610857016","https://openalex.org/W2903417164","https://openalex.org/W2911126262","https://openalex.org/W2951506174","https://openalex.org/W2963142433","https://openalex.org/W2963355980","https://openalex.org/W2963595145","https://openalex.org/W2963687408","https://openalex.org/W2964095333","https://openalex.org/W2964275228","https://openalex.org/W2964321699","https://openalex.org/W2976645955","https://openalex.org/W2997280954","https://openalex.org/W2998065416","https://openalex.org/W3004833389","https://openalex.org/W3015010871","https://openalex.org/W3101974274","https://openalex.org/W3104329805","https://openalex.org/W3105146463","https://openalex.org/W4210770595","https://openalex.org/W4213367101"],"related_works":["https://openalex.org/W3177956798","https://openalex.org/W2997810156","https://openalex.org/W1606094025","https://openalex.org/W2784647309","https://openalex.org/W2094941085","https://openalex.org/W2891400210","https://openalex.org/W2189405583","https://openalex.org/W2086947326","https://openalex.org/W2900958299","https://openalex.org/W2963651118","https://openalex.org/W1603156911","https://openalex.org/W3128753935","https://openalex.org/W2755410691","https://openalex.org/W3035879692","https://openalex.org/W3040803707","https://openalex.org/W2949165043","https://openalex.org/W91749453","https://openalex.org/W1823873661","https://openalex.org/W2735319320","https://openalex.org/W2906421926"],"abstract_inverted_index":{"is":[0,50],"the":[1,14,41,44],"ambient":[2],"dimension.":[3],"We":[4],"demonstrate":[5],"this":[6],"result":[7],"numerically,":[8],"and":[9,17,31],"show":[10],"that":[11],"in":[12],"contrast,":[13],"popular":[15],"row-stochastic":[16],"symmetric":[18],"normalizations":[19],"behave":[20],"unfavorably":[21],"under":[22],"heteroskedastic":[23],"noise.":[24],"Furthermore,":[25],"we":[26],"provide":[27],"examples":[28],"of":[29,43],"simulated":[30],"experimental":[32],"single-cell":[33],"RNA":[34],"sequence":[35],"data":[36],"with":[37],"intrinsic":[38],"heteroskedasticity,":[39],"where":[40],"advantage":[42],"doubly-stochastic":[45],"normalization":[46],"for":[47],"exploratory":[48],"analysis":[49],"evident.":[51]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}