{"id":"https://openalex.org/W7164372130","doi":"https://doi.org/10.1111/cgf.70465","title":"Class Angular Distortion Index for Dimensionality Reduction","display_name":"Class Angular Distortion Index for Dimensionality Reduction","publication_year":2026,"publication_date":"2026-06-11","ids":{"openalex":"https://openalex.org/W7164372130","doi":"https://doi.org/10.1111/cgf.70465"},"language":"en","primary_location":{"id":"doi:10.1111/cgf.70465","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70465","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1111/cgf.70465","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138454863","display_name":"Kaviru Gunaratne","orcid":"https://orcid.org/0009-0004-8091-9080"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kaviru Gunaratne","raw_affiliation_strings":["Technical University of Munich"],"raw_orcid":"https://orcid.org/0009-0004-8091-9080","affiliations":[{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003147292","display_name":"Stephen Kobourov","orcid":"https://orcid.org/0000-0002-0477-2724"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stephen Kobourov","raw_affiliation_strings":["Technical University of Munich"],"raw_orcid":"https://orcid.org/0000-0002-0477-2724","affiliations":[{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101504842","display_name":"Jacob Miller","orcid":"https://orcid.org/0000-0002-0567-785X"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jacob Miller","raw_affiliation_strings":["Technical University of Munich"],"raw_orcid":"https://orcid.org/0000-0002-0567-785X","affiliations":[{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":{"value":3710,"currency":"USD","value_usd":3710},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.7515976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10799","display_name":"Data Visualization and Analytics","score":0.4787999987602234,"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"}},"topics":[{"id":"https://openalex.org/T10799","display_name":"Data Visualization and Analytics","score":0.4787999987602234,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.1485999971628189,"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"}},{"id":"https://openalex.org/T12859","display_name":"Cell Image Analysis Techniques","score":0.03660000115633011,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"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/metric","display_name":"Metric (unit)","score":0.6414999961853027},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.6068000197410583},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5879999995231628},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5715000033378601},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.5637999773025513},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5426999926567078},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4984000027179718},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4772999882698059}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6414999961853027},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.6068000197410583},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5879999995231628},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.5637999773025513},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5426999926567078},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5121999979019165},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4984000027179718},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47769999504089355},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4772999882698059},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.47620001435279846},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4702000021934509},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34369999170303345},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C92835128","wikidata":"https://www.wikidata.org/wiki/Q1277447","display_name":"Hierarchical clustering","level":3,"score":0.2558000087738037},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/cgf.70465","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70465","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1111/cgf.70465","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70465","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1987971958","https://openalex.org/W2012343510","https://openalex.org/W2051224630","https://openalex.org/W2070246124","https://openalex.org/W2097308346","https://openalex.org/W2100437550","https://openalex.org/W2103560185","https://openalex.org/W2112796928","https://openalex.org/W2119452648","https://openalex.org/W2120043163","https://openalex.org/W2129066856","https://openalex.org/W2169371330","https://openalex.org/W2294798173","https://openalex.org/W2542768043","https://openalex.org/W2807795618","https://openalex.org/W2891575196","https://openalex.org/W2916041164","https://openalex.org/W2963988212","https://openalex.org/W2975605169","https://openalex.org/W2996274328","https://openalex.org/W3008385743","https://openalex.org/W3183807820","https://openalex.org/W3186838184","https://openalex.org/W3197209004","https://openalex.org/W4205622916","https://openalex.org/W4235169531","https://openalex.org/W4388286222","https://openalex.org/W4389988539","https://openalex.org/W4390761396","https://openalex.org/W4399585227","https://openalex.org/W4409748645","https://openalex.org/W4410606900","https://openalex.org/W4410607071","https://openalex.org/W4410777908","https://openalex.org/W4413553509","https://openalex.org/W4413878681","https://openalex.org/W4415816808","https://openalex.org/W4416707525","https://openalex.org/W6925984282","https://openalex.org/W7117530631","https://openalex.org/W7125865444"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Dimensionality":[1],"reduction":[2],"(DR)":[3],"techniques":[4,59],"are":[5],"often":[6],"characterized":[7],"by":[8],"whether":[9],"they":[10],"preserve":[11],"global,":[12],"high\u2010level":[13],"structures":[14],"in":[15,25,47,58,79,107],"the":[16,48,80,85,102],"data":[17,118],"or":[18,53,74],"local,":[19],"neighborhood":[20],"structures.":[21],"This":[22],"distinction":[23],"matters":[24],"visualization:":[26],"global":[27],"methods":[28,34],"can":[29,35],"obscure":[30],"clusters":[31,41,78],"while":[32],"local":[33],"over\u2010emphasize":[36],"them.":[37],"Yet,":[38],"even":[39],"when":[40],"appear":[42],"distinct,":[43],"their":[44],"relative":[45],"arrangement":[46],"projection":[49],"may":[50],"be":[51],"arbitrary":[52],"misleading,":[54],"a":[55,91,108,146],"common":[56],"issue":[57],"such":[60],"as":[61],"t\u2010SNE":[62],"and":[63,116],"UMAP.":[64],"Existing":[65],"cluster":[66,72,105,121],"quality":[67],"metrics":[68,122],"either":[69],"only":[70],"measure":[71],"separability":[73],"assume":[75],"spherical,":[76],"globular":[77],"original":[81],"space.":[82],"We":[83,110,142],"introduce":[84],"Class":[86],"Angular":[87],"Distortion":[88],"Index":[89],"(CADI),":[90],"metric":[92],"that":[93],"uses":[94],"internal":[95],"angles":[96],"among":[97],"point":[98],"triples":[99],"to":[100],"determine":[101],"faithfulness":[103],"of":[104],"organization":[106],"projection.":[109],"show":[111],"cases":[112],"on":[113,133],"both":[114],"real":[115],"synthetic":[117],"where":[119],"existing":[120],"fail,":[123],"but":[124],"CADI":[125,136],"provides":[126],"an":[127],"interpretable":[128],"result.":[129],"Since":[130],"it":[131],"relies":[132],"computing":[134],"angles,":[135],"is":[137],"also":[138],"differentiable,":[139],"enabling":[140],"optimization.":[141],"demonstrate":[143],"this":[144],"with":[145],"CADI\u2010based":[147],"DR":[148],"technique.":[149]},"counts_by_year":[],"updated_date":"2026-06-12T06:25:57.316018","created_date":"2026-06-12T00:00:00"}
