{"id":"https://openalex.org/W2912612061","doi":"https://doi.org/10.1007/978-3-030-46150-8_8","title":"Heavy-Tailed Kernels Reveal a Finer Cluster Structure in t-SNE Visualisations","display_name":"Heavy-Tailed Kernels Reveal a Finer Cluster Structure in t-SNE Visualisations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2912612061","doi":"https://doi.org/10.1007/978-3-030-46150-8_8","mag":"2912612061","pmid":"https://pubmed.ncbi.nlm.nih.gov/33103160"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-46150-8_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-46150-8_8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-46150-8_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-46150-8_8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Dmitry Kobak","orcid":null},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dmitry Kobak","raw_affiliation_strings":["Institute for Ophthalmic Research, University of T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Ophthalmic Research, University of T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"middle","author":{"id":null,"display_name":"George Linderman","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":false,"raw_author_name":"George Linderman","raw_affiliation_strings":["Applied Mathematics Program, Yale University, New Haven, USA"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics Program, Yale University, New Haven, USA","institution_ids":["https://openalex.org/I32971472","https://openalex.org/I4210131439"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Stefan Steinerberger","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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stefan Steinerberger","raw_affiliation_strings":["Department of Mathematics, Yale University, New Haven, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yale University, New Haven, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yuval Kluger","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":false,"raw_author_name":"Yuval Kluger","raw_affiliation_strings":["Applied Mathematics Program, Yale University, New Haven, USA","Department of Pathology, Yale School of Medicine, New Haven, USA"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics Program, Yale University, New Haven, USA","institution_ids":["https://openalex.org/I32971472","https://openalex.org/I4210131439"]},{"raw_affiliation_string":"Department of Pathology, Yale School of Medicine, New Haven, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":null,"display_name":"Philipp Berens","orcid":null},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Philipp Berens","raw_affiliation_strings":["Institute for Ophthalmic Research, University of T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Ophthalmic Research, University of T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I8087733"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":3.9465,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.94047516,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"11906","issue":null,"first_page":"124","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.8996000289916992,"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":0.8996000289916992,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.009399999864399433,"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"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.007300000172108412,"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/kernel","display_name":"Kernel (algebra)","score":0.7200000286102295},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6320000290870667},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4878000020980835},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46480000019073486},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4542999863624573},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.44670000672340393},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.43860000371932983},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.3903000056743622}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.758899986743927},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.7200000286102295},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6320000290870667},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46480000019073486},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4542999863624573},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.44670000672340393},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.43860000371932983},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40790000557899475},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39340001344680786},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.3903000056743622},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3425000011920929},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.337799996137619},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C172367668","wikidata":"https://www.wikidata.org/wiki/Q6504956","display_name":"Data visualization","level":3,"score":0.2648000121116638},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-030-46150-8_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-46150-8_8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-46150-8_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmid:33103160","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33103160","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":"Machine learning and knowledge discovery in databases : European Conference, ECML PKDD ... : proceedings. ECML PKDD (Conference)","raw_type":null},{"id":"pmh:oai:arXiv.org:1902.05804","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.05804","pdf_url":"https://arxiv.org/pdf/1902.05804","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":"pmh:oai:pubmedcentral.nih.gov:7582035","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7582035","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mach Learn Knowl Discov Databases","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-46150-8_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-46150-8_8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-46150-8_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1311014374","display_name":null,"funder_award_id":"1763179","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G1752525184","display_name":null,"funder_award_id":"FKZ 01GQ1601","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G2680112628","display_name":null,"funder_award_id":"GM007205","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G2923856803","display_name":null,"funder_award_id":"(BE5601/4-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3683686169","display_name":null,"funder_award_id":"U19MH114830","funder_id":"https://openalex.org/F4320337346","funder_display_name":"National Institute of Mental Health"},{"id":"https://openalex.org/G4568914905","display_name":null,"funder_award_id":"01IS18052","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G4667119938","display_name":null,"funder_award_id":"U19MH11483","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G4760074400","display_name":null,"funder_award_id":"U19MH114830","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G5168466499","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G5434309996","display_name":null,"funder_award_id":"DMS-1763179","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5561132364","display_name":null,"funder_award_id":"T32GM007205","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5794671194","display_name":null,"funder_award_id":"BE5601/4-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7225624288","display_name":null,"funder_award_id":"This work was","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G7242631534","display_name":null,"funder_award_id":"T32GM007205","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G7245488881","display_name":null,"funder_award_id":"01GQ1601, 01IS18052C","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G7284847551","display_name":null,"funder_award_id":"01IS18052C","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G7345195344","display_name":null,"funder_award_id":"01GQ1601","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G762232396","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"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"},{"id":"https://openalex.org/G7907426250","display_name":null,"funder_award_id":"390727645","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8128963897","display_name":null,"funder_award_id":"EXC 2064","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"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/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337346","display_name":"National Institute of Mental Health","ror":"https://ror.org/04xeg9z08"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2912612061.pdf","grobid_xml":"https://content.openalex.org/works/W2912612061.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1982729887","https://openalex.org/W1997780235","https://openalex.org/W2542768043","https://openalex.org/W2889326414","https://openalex.org/W2949693884","https://openalex.org/W2950976066","https://openalex.org/W2951527381","https://openalex.org/W2987322729","https://openalex.org/W2989747508","https://openalex.org/W2990200213","https://openalex.org/W3105146463","https://openalex.org/W4231376616"],"related_works":[],"abstract_inverted_index":{"T-distributed":[0],"stochastic":[1],"neighbour":[2],"embedding":[3],"(t-SNE)":[4],"is":[5,98],"a":[6,48],"widely":[7],"used":[8],"data":[9,115],"visualisation":[10],"technique.":[11],"It":[12],"differs":[13],"from":[14],"its":[15],"predecessor":[16],"SNE":[17,64],"by":[18,28],"the":[19,23,29,34,71,89,106,124,134,144,148,156,160],"low-dimensional":[20],"similarity":[21],"kernel:":[22],"Gaussian":[24],"kernel":[25,50,150],"was":[26],"replaced":[27],"heavy-tailed":[30],"Cauchy":[31],"kernel,":[32],"solving":[33],"'crowding":[35],"problem'":[36],"of":[37,45,55,109,147,159],"SNE.":[38],"Here,":[39],"we":[40,80,140],"develop":[41],"an":[42,52],"efficient":[43],"implementation":[44],"t-SNE":[46,149],"for":[47],"t-distribution":[49],"with":[51,58],"arbitrary":[53],"degree":[54],"freedom":[56],"<i>\u03bd</i>,":[57],"<i>\u03bd</i>":[59,66,83],"\u2192":[60],"\u221e":[61],"corresponding":[62,69],"to":[63,70,131],"and":[65,77,92,123],"=":[67],"1":[68,85],"standard":[72,101],"t-SNE.":[73,102],"Using":[74],"theoretical":[75],"analysis":[76],"toy":[78],"examples,":[79],"show":[81],"that":[82,97,133,142],"<":[84],"can":[86,151],"further":[87,104],"reduce":[88],"crowding":[90],"problem":[91],"reveal":[93],"finer":[94],"cluster":[95,157],"structure":[96,158],"invisible":[99],"in":[100],"We":[103,127],"demonstrate":[105],"striking":[107],"effect":[108],"heavier-tailed":[110],"kernels":[111],"on":[112],"large":[113],"real-life":[114],"sets":[116],"such":[117],"as":[118],"MNIST,":[119],"single-cell":[120],"RNA-sequencing":[121],"data,":[122],"HathiTrust":[125],"library.":[126],"use":[128],"domain":[129],"knowledge":[130],"confirm":[132],"revealed":[135],"clusters":[136],"are":[137],"meaningful.":[138],"Overall,":[139],"argue":[141],"modifying":[143],"tail":[145],"heaviness":[146],"yield":[152],"additional":[153],"insight":[154],"into":[155],"data.":[161]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-02-21T00:00:00"}
