{"id":"https://openalex.org/W7133348044","doi":"https://doi.org/10.1016/j.ic.2026.105430","title":"Impossibility of depth reduction in explainable clustering","display_name":"Impossibility of depth reduction in explainable clustering","publication_year":2026,"publication_date":"2026-03-04","ids":{"openalex":"https://openalex.org/W7133348044","doi":"https://doi.org/10.1016/j.ic.2026.105430"},"language":"en","primary_location":{"id":"doi:10.1016/j.ic.2026.105430","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ic.2026.105430","pdf_url":null,"source":{"id":"https://openalex.org/S59933527","display_name":"Information and Computation","issn_l":"0890-5401","issn":["0890-5401","1090-2651"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.ic.2026.105430","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006452312","display_name":"Chengyuan Deng","orcid":"https://orcid.org/0000-0002-2586-3430"},"institutions":[{"id":"https://openalex.org/I4210096112","display_name":"Rutgers Sexual and Reproductive Health and Rights","ror":"https://ror.org/00rcvgx40","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210096112"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Chengyuan Deng","raw_affiliation_strings":["Rutgers University,"],"affiliations":[{"raw_affiliation_string":"Rutgers University,","institution_ids":["https://openalex.org/I4210096112"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085478109","display_name":"Surya Teja Gavva","orcid":"https://orcid.org/0000-0003-0845-5029"},"institutions":[{"id":"https://openalex.org/I4210096112","display_name":"Rutgers Sexual and Reproductive Health and Rights","ror":"https://ror.org/00rcvgx40","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210096112"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Surya Teja Gavva","raw_affiliation_strings":["Rutgers University,"],"affiliations":[{"raw_affiliation_string":"Rutgers University,","institution_ids":["https://openalex.org/I4210096112"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Karthik C\u2024\u202fS\u2024","orcid":"https://orcid.org/0000-0001-9105-364X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karthik C\u2024\u202fS\u2024","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083363461","display_name":"Parth Patel","orcid":"https://orcid.org/0000-0001-5207-2776"},"institutions":[{"id":"https://openalex.org/I4210096112","display_name":"Rutgers Sexual and Reproductive Health and Rights","ror":"https://ror.org/00rcvgx40","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210096112"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Parth Patel","raw_affiliation_strings":["Rutgers University,"],"affiliations":[{"raw_affiliation_string":"Rutgers University,","institution_ids":["https://openalex.org/I4210096112"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065114509","display_name":"Adarsh Srinivasan","orcid":"https://orcid.org/0000-0003-0288-4818"},"institutions":[{"id":"https://openalex.org/I4210096112","display_name":"Rutgers Sexual and Reproductive Health and Rights","ror":"https://ror.org/00rcvgx40","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210096112"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Adarsh Srinivasan","raw_affiliation_strings":["Rutgers University,"],"affiliations":[{"raw_affiliation_string":"Rutgers University,","institution_ids":["https://openalex.org/I4210096112"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5006452312","https://openalex.org/A5065114509","https://openalex.org/A5083363461","https://openalex.org/A5085478109"],"corresponding_institution_ids":["https://openalex.org/I4210096112"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":{"value":2630,"currency":"USD","value_usd":2630},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.6085889,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"310","issue":null,"first_page":"105430","last_page":"105430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.18080000579357147,"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"}},"topics":[{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.18080000579357147,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.09709999710321426,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.05770000070333481,"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/cluster-analysis","display_name":"Cluster analysis","score":0.7286999821662903},{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.6294000148773193},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5368000268936157},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4903999865055084},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4603999853134155},{"id":"https://openalex.org/keywords/decision-tree","display_name":"Decision tree","score":0.3874000012874603},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.3779999911785126},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.36320000886917114}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7317000031471252},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7286999821662903},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.6294000148773193},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5368000268936157},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5340999960899353},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4903999865055084},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4603999853134155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4187000095844269},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3779999911785126},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.36320000886917114},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C207024777","wikidata":"https://www.wikidata.org/wiki/Q621673","display_name":"Search tree","level":3,"score":0.31859999895095825},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.2946999967098236},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2531999945640564}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.ic.2026.105430","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ic.2026.105430","pdf_url":null,"source":{"id":"https://openalex.org/S59933527","display_name":"Information and Computation","issn_l":"0890-5401","issn":["0890-5401","1090-2651"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.ic.2026.105430","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ic.2026.105430","pdf_url":null,"source":{"id":"https://openalex.org/S59933527","display_name":"Information and Computation","issn_l":"0890-5401","issn":["0890-5401","1090-2651"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7538558840751648,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1973264045","https://openalex.org/W1995718774","https://openalex.org/W2044028871","https://openalex.org/W2437551018","https://openalex.org/W2910705748","https://openalex.org/W2981838741","https://openalex.org/W4311139009","https://openalex.org/W4386424378","https://openalex.org/W7133228322"],"related_works":[],"abstract_inverted_index":{"Over":[0],"the":[1,18,30,41,61,64,82,87,95,101,141,163,173],"last":[2],"few":[3],"years":[4],"Explainable":[5],"Clustering":[6],"has":[7,159],"gathered":[8],"a":[9,35,57,114,126],"lot":[10],"of":[11,20,63,72,129,145,152,166],"attention.":[12],"Dasgupta":[13],"et":[14,52],"al.":[15,53],"[ICML\u201920]":[16],"initiated":[17],"study":[19],"explainable":[21],"k":[22,25,102,105,131,135,137,156,174],"-means":[23,103],"and":[24,104],"-median":[26,106,138],"clustering":[27,143],"problems":[28],"where":[29],"explanation":[31,96],"is":[32,125],"captured":[33],"by":[34],"threshold":[36],"decision":[37,65,127,150],"tree":[38,66,128,151],"which":[39,123],"partitions":[40],"space":[42],"at":[43],"each":[44],"node":[45],"using":[46],"axis":[47],"parallel":[48],"hyperplanes.":[49],"Recently,":[50],"Laber":[51],"[Pattern":[54],"Recognition\u201923]":[55],"made":[56],"case":[58],"to":[59,172],"consider":[60],"depth":[62,92,130,153],"as":[67,177],"an":[68],"additional":[69],"complexity":[70],"measure":[71],"interest.":[73],"In":[74],"this":[75],"work,":[76],"we":[77,109],"prove":[78],"that":[79,111],"even":[80],"when":[81],"input":[83],"points":[84],"are":[85],"in":[86,94,100],"Euclidean":[88],"plane,":[89],"then":[90],"any":[91],"reduction":[93],"incurs":[97],"unbounded":[98,160],"loss":[99],"cost.":[107],"Formally,":[108],"show":[110],"there":[112,124],"exists":[113],"data":[115],"set":[116],"X":[117,146],"\u2286":[118],"R":[119],"2":[120],",":[121,147],"for":[122],"\u2212":[132,157],"1":[133,158],"whose":[134],"-means/":[136],"cost":[139,144,161,165],"matches":[140],"optimal":[142,164],"but":[148],"every":[149],"less":[154],"than":[155],"w.r.t.":[162],"clustering.":[167],"We":[168],"extend":[169],"our":[170],"results":[171],"-center":[175],"objective":[176],"well,":[178],"albeit":[179],"with":[180],"weaker":[181],"guarantees.":[182]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2026-03-04T00:00:00"}