Clustering with the Average Silhouette Width
The Average Silhouette Width (ASW) is a popular cluster validation index to estimate the number of clusters. The question whether it also is suitable as a general objective function to be optimized for finding a clustering is addressed. Two algorithms (the standard version OSil and a fast version FO...
Saved in:
| Published in | Computational statistics & data analysis Vol. 158; p. 107190 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.06.2021
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The Average Silhouette Width (ASW) is a popular cluster validation index to estimate the number of clusters. The question whether it also is suitable as a general objective function to be optimized for finding a clustering is addressed. Two algorithms (the standard version OSil and a fast version FOSil) are proposed, and they are compared with existing clustering methods in an extensive simulation study covering known and unknown numbers of clusters. Real data sets are analysed, partly exploring the use of the new methods with non-Euclidean distances. The ASW is shown to satisfy some axioms that have been proposed for cluster quality functions. The new methods prove useful and sensible in many cases, but some weaknesses are also highlighted. These also concern the use of the ASW for estimating the number of clusters together with other methods, which is of general interest due to the popularity of the ASW for this task. |
|---|---|
| AbstractList | The Average Silhouette Width (ASW) is a popular cluster validation index to estimate the number of clusters. The question whether it also is suitable as a general objective function to be optimized for finding a clustering is addressed. Two algorithms (the standard version OSil and a fast version FOSil) are proposed, and they are compared with existing clustering methods in an extensive simulation study covering known and unknown numbers of clusters. Real data sets are analysed, partly exploring the use of the new methods with non-Euclidean distances. The ASW is shown to satisfy some axioms that have been proposed for cluster quality functions. The new methods prove useful and sensible in many cases, but some weaknesses are also highlighted. These also concern the use of the ASW for estimating the number of clusters together with other methods, which is of general interest due to the popularity of the ASW for this task. |
| ArticleNumber | 107190 |
| Author | Batool, Fatima Hennig, Christian |
| Author_xml | – sequence: 1 givenname: Fatima orcidid: 0000-0003-1354-0375 surname: Batool fullname: Batool, Fatima email: fatima.batool.14@ucl.ac.uk organization: Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, United Kingdom – sequence: 2 givenname: Christian surname: Hennig fullname: Hennig, Christian email: christian.hennig@unibo.it organization: Dipartimento di Scienze Statistiche “Paolo Fortunati”, Universita di Bologna, Bologna, Via delle belle Arti, 41, 40126, Italy |
| BookMark | eNp9kD1PwzAQhi1UJNrCH2DKyECK7Th2LLFUFV9SJQZAjJZjX1pXaVJsp4h_T6IwMXR6daf3OemeGZo0bQMIXRO8IJjwu93CBKsXFFPSLwSR-AxNSSFoKrKcTtC0L4lUMpFdoFkIO4wxZaKYottV3YUI3jWb5NvFbRK3kCyP4PUGkjdXb9sOYoTk09m4vUTnla4DXP3lHH08PryvntP169PLarlOTSZETLUpidVEgujHSmLJGRgreTUELwWupMwNKzJmuDC2yssSLJHCSkpNxWg2Rzfj3YNvvzoIUe1dMFDXuoG2C4ryjDNW5Jz31WKsGt-G4KFSxkUdXdtEr12tCFaDILVTgyA1CFKjoB6l_9CDd3vtf05D9yME_f9HB14F46AxYJ0HE5Vt3Sn8F03xgIw |
| CitedBy_id | crossref_primary_10_1016_j_ecosta_2023_03_002 crossref_primary_10_1111_spol_13080 crossref_primary_10_1245_s10434_024_16860_y crossref_primary_10_1371_journal_pone_0300358 crossref_primary_10_1007_s12145_024_01303_9 crossref_primary_10_1016_j_patcog_2022_109144 crossref_primary_10_3389_fpls_2024_1468395 crossref_primary_10_1016_j_cor_2022_106135 crossref_primary_10_1097_CCE_0000000000000566 crossref_primary_10_1051_e3sconf_202449604001 crossref_primary_10_1093_geronb_gbad108 crossref_primary_10_1108_JEPP_01_2023_0007 crossref_primary_10_1016_j_gecco_2024_e03144 crossref_primary_10_2139_ssrn_4141620 crossref_primary_10_1111_mms_13013 crossref_primary_10_1186_s40536_023_00164_w crossref_primary_10_1038_s42256_022_00518_z crossref_primary_10_1186_s13059_024_03401_9 crossref_primary_10_1016_j_isci_2022_104480 crossref_primary_10_1016_j_xpro_2023_102548 crossref_primary_10_1007_s10518_024_02003_x crossref_primary_10_14718_revfinanzpolitecon_v16_n2_2024_4 crossref_primary_10_1080_19312458_2023_2242774 crossref_primary_10_1007_s41748_024_00516_8 crossref_primary_10_3390_rs16152712 crossref_primary_10_1177_01902725241311306 crossref_primary_10_1109_ACCESS_2024_3350791 crossref_primary_10_1080_14459795_2022_2135753 crossref_primary_10_1111_sjos_12692 crossref_primary_10_1016_j_spasta_2023_100785 crossref_primary_10_1007_s10479_023_05321_6 crossref_primary_10_1186_s12913_023_10218_y crossref_primary_10_1016_j_is_2023_102290 crossref_primary_10_1038_s44168_023_00080_3 crossref_primary_10_1016_j_compbiomed_2025_109709 crossref_primary_10_1016_j_fcr_2023_108945 crossref_primary_10_1080_14697688_2024_2412687 crossref_primary_10_1007_s11356_023_31414_7 crossref_primary_10_1002_lary_31272 crossref_primary_10_1016_j_ins_2022_12_057 crossref_primary_10_1007_s11135_021_01263_y crossref_primary_10_1016_j_heliyon_2024_e32479 crossref_primary_10_1109_ACCESS_2021_3071654 crossref_primary_10_1515_ijb_2023_0061 crossref_primary_10_1073_pnas_2313719121 crossref_primary_10_1016_j_envc_2025_101105 crossref_primary_10_1016_j_rineng_2022_100544 crossref_primary_10_1016_j_ijepes_2022_108813 crossref_primary_10_1016_j_tibtech_2022_02_005 crossref_primary_10_1007_s12065_021_00667_x crossref_primary_10_3389_fpubh_2023_1298693 crossref_primary_10_1186_s40462_023_00386_1 crossref_primary_10_1002_pca_3436 crossref_primary_10_1007_s11042_023_17129_4 crossref_primary_10_2147_NSS_S455705 crossref_primary_10_1038_s41467_021_25534_2 crossref_primary_10_1186_s12885_024_13387_z crossref_primary_10_3390_nursrep14030126 crossref_primary_10_3390_land10060589 crossref_primary_10_1109_ACCESS_2025_3527715 crossref_primary_10_3233_WOR_230307 crossref_primary_10_1007_s10639_024_12793_x crossref_primary_10_1016_j_ijar_2022_11_021 crossref_primary_10_1016_j_jcmg_2024_06_013 crossref_primary_10_1136_bjo_2023_323592 crossref_primary_10_1007_s10618_024_01086_z crossref_primary_10_1109_ACCESS_2023_3235724 crossref_primary_10_1016_j_procs_2023_10_268 crossref_primary_10_1186_s12874_024_02427_8 crossref_primary_10_1016_j_jss_2022_111538 crossref_primary_10_1002_ppul_26712 crossref_primary_10_1177_14614456241237378 crossref_primary_10_1016_j_eswa_2024_125369 crossref_primary_10_1080_19466315_2024_2308882 crossref_primary_10_3390_axioms11120674 crossref_primary_10_1016_j_cie_2022_107975 crossref_primary_10_1186_s40163_023_00186_3 crossref_primary_10_1007_s12530_023_09530_z crossref_primary_10_1002_joe_22230 crossref_primary_10_1177_08862605221137712 crossref_primary_10_3390_healthcare12151499 crossref_primary_10_1016_j_jclepro_2025_144792 crossref_primary_10_1016_j_oceaneng_2024_118492 crossref_primary_10_1007_s00520_024_08500_8 crossref_primary_10_1109_OJCS_2025_3545261 crossref_primary_10_1016_j_jneumeth_2023_110049 crossref_primary_10_18069_firatsbed_1029895 crossref_primary_10_1515_snde_2023_0024 crossref_primary_10_1002_eng2_12793 crossref_primary_10_1371_journal_pone_0313425 crossref_primary_10_3390_d15030386 |
| Cites_doi | 10.1093/comjnl/41.8.578 10.1016/j.cell.2016.01.047 10.1109/TIT.1982.1056489 10.1080/0094965031000136012 10.1080/01621459.1963.10500845 10.1111/1467-9868.00293 10.1007/BF01908075 10.1093/comjnl/11.2.177 10.1016/0022-5193(67)90046-X 10.1175/JCLI-D-12-00836.1 10.1016/0377-0427(87)90125-7 10.1126/science.aaa1934 10.1016/j.patcog.2013.02.016 10.1007/s11222-015-9566-5 10.1080/03610927408827101 10.1016/0031-3203(73)90048-4 10.1016/j.stem.2015.09.011 10.1016/j.patrec.2015.04.009 10.1007/s10208-012-9141-9 10.1093/biomet/58.1.91 10.1101/gr.177725.114 10.1016/0031-0182(93)90084-V 10.1016/j.patcog.2012.07.021 10.1016/j.jmva.2007.07.002 |
| ContentType | Journal Article |
| Copyright | 2021 Elsevier B.V. |
| Copyright_xml | – notice: 2021 Elsevier B.V. |
| DBID | AAYXX CITATION 7S9 L.6 |
| DOI | 10.1016/j.csda.2021.107190 |
| DatabaseName | CrossRef AGRICOLA AGRICOLA - Academic |
| DatabaseTitle | CrossRef AGRICOLA AGRICOLA - Academic |
| DatabaseTitleList | AGRICOLA |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Statistics |
| EISSN | 1872-7352 |
| ExternalDocumentID | 10_1016_j_csda_2021_107190 S0167947321000244 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1OL 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO AAYFN ABAOU ABBOA ABFNM ABMAC ABTAH ABUCO ABXDB ABYKQ ACAZW ACDAQ ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADGUI ADJOM ADMUD ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHZHX AI. AIALX AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD APLSM ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA GBOLZ HAMUX HLZ HMJ HVGLF HZ~ H~9 IHE J1W JJJVA KOM LG9 LY1 M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SBC SDF SDG SDS SES SEW SME SPC SPCBC SSB SSD SST SSV SSW SSZ T5K VH1 VOH WUQ XPP ZMT ZY4 ~02 ~G- AAHBH AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACRPL ACVFH ADCNI ADNMO ADXHL AEIPS AEUPX AFJKZ AFPUW AFXIZ AGCQF AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP BNPGV CITATION SSH 7S9 EFKBS L.6 |
| ID | FETCH-LOGICAL-c377t-acb1da19e7377f90964ecd96f4ecd6b70f995c4834c67cdf5bbed197d922cf423 |
| IEDL.DBID | .~1 |
| ISSN | 0167-9473 |
| IngestDate | Tue Aug 05 10:14:34 EDT 2025 Thu Apr 24 22:53:53 EDT 2025 Tue Jul 01 02:24:35 EDT 2025 Fri Feb 23 02:47:18 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Axiomatic clustering Partitioning around medoids Number of clusters Distance-based clustering |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c377t-acb1da19e7377f90964ecd96f4ecd6b70f995c4834c67cdf5bbed197d922cf423 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ORCID | 0000-0003-1354-0375 |
| OpenAccessLink | https://hdl.handle.net/11585/848943 |
| PQID | 2636448566 |
| PQPubID | 24069 |
| ParticipantIDs | proquest_miscellaneous_2636448566 crossref_citationtrail_10_1016_j_csda_2021_107190 crossref_primary_10_1016_j_csda_2021_107190 elsevier_sciencedirect_doi_10_1016_j_csda_2021_107190 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | June 2021 2021-06-00 20210601 |
| PublicationDateYYYYMMDD | 2021-06-01 |
| PublicationDate_xml | – month: 06 year: 2021 text: June 2021 |
| PublicationDecade | 2020 |
| PublicationTitle | Computational statistics & data analysis |
| PublicationYear | 2021 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Correa-Morris (b8) 2013; 46 Ackerman, Ben-David (b1) 2009 Wright (b38) 1973; 5 Maechler, Rousseeuw, Struyf, Hubert, Hornik (b27) 2017 Hennig (b14) 2008; 99 Ward (b37) 1963; 58 Shi (b33) 1993; 105 Carlsson, Mémoli (b7) 2013; 13 Hubert, Arabie (b18) 1985; 2 Kaufman, Rousseeuw (b21) 1990 Tibshirani, Walther, Hastie (b35) 2001; 63 Hennig (b15) 2015; 64 Lun, McCarthy, Marioni (b26) 2016 Lloyd (b25) 1982; 28 Hennig, Meila, Murtagh, Rocci (b17) 2015 Fraley, Raftery (b10) 1998; 41 Rubin (b31) 1967; 15 Kolodziejczyk, Kim, Tsang, Ilicic, Henriksson, Natarajan, Tuck, Gao, Bühler, Liu (b23) 2015; 17 Zadeh, Ben-David (b40) 2009 Jardine, Sibson (b19) 1968; 11 Zeileis, Hornik, Smola, Karatzoglou (b41) 2004; 11 Ng, Jordan, Weiss (b29) 2001 Hartigan, Wong (b13) 1979; 28 Van der Laan, Pollard, Bryan (b24) 2003; 73 Fisher, Ness (b9) 1971; 58 Kaufman, Rousseeuw (b20) 1987 Halkidi, Vazirgiannis, Hennig (b12) 2015 Bernard, Naveau, Vrac, Mestre (b4) 2013; 26 Scrucca, Fop, Murphy, Raftery (b32) 2017; 8 Zeisel, Muñoz Manchado, Codeluppi, Lönnerberg, La Manno, Juréus, Marques, Munguba, He, Betsholtz (b42) 2015; 347 Sokal, Michener (b34) 1958; 38 Batool (b3) 2020 Caliński, Harabasz (b6) 1974; 3 Martinez-Ortega, Delgado, Albach, Elena-Rossello, Rico (b28) 2004; 29 Von Luxburg, U., Williamson, R.C., Guyon, I., 2012. Clustering: Science or art? In: Proceedings of ICML Workshop on Unsupervised and Transfer Learning, pp. 65–79. Goolam, Scialdone, Graham, Macaulay, Jedrusik, Hupalowska, Voet, Marioni, Zernicka-Goetz (b11) 2016; 165 Hennig, Lin (b16) 2015; 25 Arbelaitz, Gurrutxaga, Muguerza, Perez, Perona (b2) 2012; 46 Biase, Cao, Zhong (b5) 2014; 24 Kleinberg (b22) 2003 Rousseeuw (b30) 1987; 20 Yan, Yang, Guo, Yang, Wu, Li, Liu, Lian, Zheng, Yan (b39) 2013; 20 Rubin (10.1016/j.csda.2021.107190_b31) 1967; 15 Bernard (10.1016/j.csda.2021.107190_b4) 2013; 26 Lloyd (10.1016/j.csda.2021.107190_b25) 1982; 28 Yan (10.1016/j.csda.2021.107190_b39) 2013; 20 Tibshirani (10.1016/j.csda.2021.107190_b35) 2001; 63 Hennig (10.1016/j.csda.2021.107190_b17) 2015 Scrucca (10.1016/j.csda.2021.107190_b32) 2017; 8 Shi (10.1016/j.csda.2021.107190_b33) 1993; 105 Zeileis (10.1016/j.csda.2021.107190_b41) 2004; 11 Biase (10.1016/j.csda.2021.107190_b5) 2014; 24 Arbelaitz (10.1016/j.csda.2021.107190_b2) 2012; 46 Fisher (10.1016/j.csda.2021.107190_b9) 1971; 58 Goolam (10.1016/j.csda.2021.107190_b11) 2016; 165 Hennig (10.1016/j.csda.2021.107190_b15) 2015; 64 Wright (10.1016/j.csda.2021.107190_b38) 1973; 5 Ng (10.1016/j.csda.2021.107190_b29) 2001 Carlsson (10.1016/j.csda.2021.107190_b7) 2013; 13 Sokal (10.1016/j.csda.2021.107190_b34) 1958; 38 10.1016/j.csda.2021.107190_b36 Ward (10.1016/j.csda.2021.107190_b37) 1963; 58 Zadeh (10.1016/j.csda.2021.107190_b40) 2009 Halkidi (10.1016/j.csda.2021.107190_b12) 2015 Kolodziejczyk (10.1016/j.csda.2021.107190_b23) 2015; 17 Van der Laan (10.1016/j.csda.2021.107190_b24) 2003; 73 Batool (10.1016/j.csda.2021.107190_b3) 2020 Martinez-Ortega (10.1016/j.csda.2021.107190_b28) 2004; 29 Ackerman (10.1016/j.csda.2021.107190_b1) 2009 Fraley (10.1016/j.csda.2021.107190_b10) 1998; 41 Hubert (10.1016/j.csda.2021.107190_b18) 1985; 2 Hennig (10.1016/j.csda.2021.107190_b14) 2008; 99 Lun (10.1016/j.csda.2021.107190_b26) 2016 Maechler (10.1016/j.csda.2021.107190_b27) 2017 Zeisel (10.1016/j.csda.2021.107190_b42) 2015; 347 Kaufman (10.1016/j.csda.2021.107190_b20) 1987 Kaufman (10.1016/j.csda.2021.107190_b21) 1990 Kleinberg (10.1016/j.csda.2021.107190_b22) 2003 Rousseeuw (10.1016/j.csda.2021.107190_b30) 1987; 20 Jardine (10.1016/j.csda.2021.107190_b19) 1968; 11 Caliński (10.1016/j.csda.2021.107190_b6) 1974; 3 Hennig (10.1016/j.csda.2021.107190_b16) 2015; 25 Correa-Morris (10.1016/j.csda.2021.107190_b8) 2013; 46 Hartigan (10.1016/j.csda.2021.107190_b13) 1979; 28 |
| References_xml | – volume: 28 start-page: 129 year: 1982 end-page: 137 ident: b25 article-title: Least squares quantization in pcm publication-title: IEEE Trans. Inform. Theory – start-page: 595 year: 2015 end-page: 618 ident: b12 article-title: Method-independent indices for cluster validation and estimating the number of clusters publication-title: Handbook of Cluster Analysis – volume: 165 start-page: 61 year: 2016 end-page: 74 ident: b11 article-title: Heterogeneity in oct4 and sox2 targets biases cell fate in 4-cell mouse embryos publication-title: Cell – volume: 38 start-page: 1409 year: 1958 end-page: 1438 ident: b34 article-title: A statistical method for evaluating systematic relationships publication-title: Univ. Kansas Sci. Bull. – volume: 20 year: 2013 ident: b39 article-title: Single-cell rna-seq profiling of human preimplantation embryos and embryonic stem cells publication-title: Nat. Struct. Mol. Biol. – reference: Von Luxburg, U., Williamson, R.C., Guyon, I., 2012. Clustering: Science or art? In: Proceedings of ICML Workshop on Unsupervised and Transfer Learning, pp. 65–79. – volume: 24 start-page: 1787 year: 2014 end-page: 1796 ident: b5 article-title: Cell fate inclination within 2-cell and 4-cell mouse embryos revealed by single-cell rna sequencing publication-title: Genome Res. – volume: 46 start-page: 243 year: 2012 end-page: 256 ident: b2 article-title: An extensive comparative study of cluster validity indices publication-title: Pattern Recognit. – volume: 3 start-page: 1 year: 1974 end-page: 27 ident: b6 article-title: A dendrite method for cluster analysis publication-title: Comm. Statist. Theory Methods – volume: 41 start-page: 578 year: 1998 end-page: 588 ident: b10 article-title: How many clusters? which clustering method? answers via model-based cluster analysis publication-title: Comput. J. – volume: 105 start-page: 199 year: 1993 end-page: 234 ident: b33 article-title: Multivariate data analysis in palaeoecology and palaeobiogeography-a review publication-title: Palaeogeogr. Palaeoclimatol. Palaeoecol. – volume: 63 start-page: 411 year: 2001 end-page: 423 ident: b35 article-title: Estimating the number of clusters in a data set via the gap statistic publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol. – volume: 25 start-page: 821 year: 2015 end-page: 833 ident: b16 article-title: Flexible parametric bootstrap for testing homogeneity against clustering and assessing the number of clusters publication-title: Stat. Comput. – volume: 5 start-page: 273 year: 1973 end-page: 282 ident: b38 article-title: A formalization of cluster analysis publication-title: Pattern Recognit. – start-page: 121 year: 2009 end-page: 128 ident: b1 article-title: Measures of clustering quality: A working set of axioms for clustering publication-title: Advances in Neural Information Processing Systems – start-page: 463 year: 2003 end-page: 470 ident: b22 article-title: An impossibility theorem for clustering publication-title: Advances in Neural Information Processing Systems – volume: 20 start-page: 53 year: 1987 end-page: 65 ident: b30 article-title: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis publication-title: J. Comput. Appl. Math. – start-page: 849 year: 2001 end-page: 856 ident: b29 article-title: On spectral clustering: Analysis and an algorithm publication-title: NIPS – volume: 11 start-page: 177 year: 1968 end-page: 184 ident: b19 article-title: The construction of hierarchic and non-hierarchic classifications publication-title: Comput. J. – volume: 2 start-page: 193 year: 1985 end-page: 218 ident: b18 article-title: Comparing partitions publication-title: J. Classification – volume: 73 start-page: 575 year: 2003 end-page: 584 ident: b24 article-title: A new partitioning around medoids algorithm publication-title: J. Stat. Comput. Simul. – volume: 46 start-page: 2548 year: 2013 end-page: 2561 ident: b8 article-title: An indication of unification for different clustering approaches publication-title: Pattern Recognit. – start-page: 639 year: 2009 end-page: 646 ident: b40 article-title: A uniqueness theorem for clustering publication-title: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence – volume: 28 start-page: 100 year: 1979 end-page: 108 ident: b13 article-title: Algorithm as 136: A k-means clustering algorithm publication-title: J. R. Stat. Soc. Ser. C. Appl. Stat. – year: 2015 ident: b17 article-title: Handbook of Cluster Analysis – volume: 15 start-page: 103 year: 1967 end-page: 144 ident: b31 article-title: Optimal classification into groups: an approach for solving the taxonomy problem publication-title: J. Theoret. Biol. – year: 1990 ident: b21 article-title: Finding Groups in Data: An Introduction to Cluster Analysis. Volume, 344 – volume: 347 start-page: 1138 year: 2015 end-page: 1142 ident: b42 article-title: Cell types in the mouse cortex and hippocampus revealed by single-cell rna-seq publication-title: Science – volume: 58 start-page: 91 year: 1971 end-page: 104 ident: b9 article-title: Admissible clustering procedures publication-title: Biometrika – volume: 64 start-page: 53 year: 2015 end-page: 62 ident: b15 article-title: What are the true clusters? publication-title: Pattern Recognit. Lett. – volume: 58 start-page: 236 year: 1963 end-page: 244 ident: b37 article-title: Hierarchical grouping to optimize an objective function publication-title: J. Amer. Statist. Assoc. – volume: 13 start-page: 221 year: 2013 end-page: 252 ident: b7 article-title: Classifying clustering schemes publication-title: Found. Comput. Math. – volume: 29 start-page: 965 year: 2004 end-page: 986 ident: b28 article-title: Species boundaries and phylogeographic patterns in cryptic taxa inferred from aflp markers: Veronica subgen. pentasepalae (scrophulariaceae) in the western mediterranean publication-title: Syst. Biol. – year: 2020 ident: b3 article-title: Initialization methods for optimum average silhouette width clustering – volume: 8 start-page: 205 year: 2017 end-page: 233 ident: b32 article-title: Mclust 5: clustering, classification and density estimation using Gaussian finite mixture models publication-title: R J. – volume: 11 start-page: 1 year: 2004 end-page: 20 ident: b41 article-title: Kernlab – an s4 package for kernel methods in r publication-title: J. Stat. Softw. – volume: 26 start-page: 7929 year: 2013 end-page: 7937 ident: b4 article-title: Clustering of maxima: Spatial dependencies among heavy rainfall in france publication-title: J. Clim. – volume: 99 start-page: 1154 year: 2008 end-page: 1176 ident: b14 article-title: Dissolution point and isolation robustness: robustness criteria for general cluster analysis methods publication-title: J. Multivariate Anal. – year: 2017 ident: b27 article-title: Cluster: Cluster analysis basics and extensions. R package version 2.0.6 – year: 1987 ident: b20 article-title: Clustering by Means of Medoids – volume: 17 start-page: 471 year: 2015 end-page: 485 ident: b23 article-title: Single cell rna-sequencing of pluripotent states unlocks modular transcriptional variation publication-title: Cell Stem Cell – start-page: 5 year: 2016 ident: b26 publication-title: A Step-By-Step Workflow for Low-Level Analysis of Single-Cell Rna-Seq Data with Bioconductor – volume: 41 start-page: 578 year: 1998 ident: 10.1016/j.csda.2021.107190_b10 article-title: How many clusters? which clustering method? answers via model-based cluster analysis publication-title: Comput. J. doi: 10.1093/comjnl/41.8.578 – volume: 165 start-page: 61 year: 2016 ident: 10.1016/j.csda.2021.107190_b11 article-title: Heterogeneity in oct4 and sox2 targets biases cell fate in 4-cell mouse embryos publication-title: Cell doi: 10.1016/j.cell.2016.01.047 – volume: 28 start-page: 129 year: 1982 ident: 10.1016/j.csda.2021.107190_b25 article-title: Least squares quantization in pcm publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.1982.1056489 – volume: 8 start-page: 205 year: 2017 ident: 10.1016/j.csda.2021.107190_b32 article-title: Mclust 5: clustering, classification and density estimation using Gaussian finite mixture models publication-title: R J. – start-page: 849 year: 2001 ident: 10.1016/j.csda.2021.107190_b29 article-title: On spectral clustering: Analysis and an algorithm – start-page: 639 year: 2009 ident: 10.1016/j.csda.2021.107190_b40 article-title: A uniqueness theorem for clustering – volume: 73 start-page: 575 year: 2003 ident: 10.1016/j.csda.2021.107190_b24 article-title: A new partitioning around medoids algorithm publication-title: J. Stat. Comput. Simul. doi: 10.1080/0094965031000136012 – volume: 58 start-page: 236 year: 1963 ident: 10.1016/j.csda.2021.107190_b37 article-title: Hierarchical grouping to optimize an objective function publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1963.10500845 – volume: 63 start-page: 411 year: 2001 ident: 10.1016/j.csda.2021.107190_b35 article-title: Estimating the number of clusters in a data set via the gap statistic publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol. doi: 10.1111/1467-9868.00293 – start-page: 595 year: 2015 ident: 10.1016/j.csda.2021.107190_b12 article-title: Method-independent indices for cluster validation and estimating the number of clusters – volume: 2 start-page: 193 year: 1985 ident: 10.1016/j.csda.2021.107190_b18 article-title: Comparing partitions publication-title: J. Classification doi: 10.1007/BF01908075 – volume: 11 start-page: 177 year: 1968 ident: 10.1016/j.csda.2021.107190_b19 article-title: The construction of hierarchic and non-hierarchic classifications publication-title: Comput. J. doi: 10.1093/comjnl/11.2.177 – volume: 15 start-page: 103 year: 1967 ident: 10.1016/j.csda.2021.107190_b31 article-title: Optimal classification into groups: an approach for solving the taxonomy problem publication-title: J. Theoret. Biol. doi: 10.1016/0022-5193(67)90046-X – volume: 26 start-page: 7929 year: 2013 ident: 10.1016/j.csda.2021.107190_b4 article-title: Clustering of maxima: Spatial dependencies among heavy rainfall in france publication-title: J. Clim. doi: 10.1175/JCLI-D-12-00836.1 – volume: 20 start-page: 53 year: 1987 ident: 10.1016/j.csda.2021.107190_b30 article-title: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(87)90125-7 – volume: 28 start-page: 100 year: 1979 ident: 10.1016/j.csda.2021.107190_b13 article-title: Algorithm as 136: A k-means clustering algorithm publication-title: J. R. Stat. Soc. Ser. C. Appl. Stat. – ident: 10.1016/j.csda.2021.107190_b36 – year: 2020 ident: 10.1016/j.csda.2021.107190_b3 – volume: 347 start-page: 1138 year: 2015 ident: 10.1016/j.csda.2021.107190_b42 article-title: Cell types in the mouse cortex and hippocampus revealed by single-cell rna-seq publication-title: Science doi: 10.1126/science.aaa1934 – volume: 46 start-page: 2548 year: 2013 ident: 10.1016/j.csda.2021.107190_b8 article-title: An indication of unification for different clustering approaches publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2013.02.016 – volume: 25 start-page: 821 year: 2015 ident: 10.1016/j.csda.2021.107190_b16 article-title: Flexible parametric bootstrap for testing homogeneity against clustering and assessing the number of clusters publication-title: Stat. Comput. doi: 10.1007/s11222-015-9566-5 – volume: 3 start-page: 1 year: 1974 ident: 10.1016/j.csda.2021.107190_b6 article-title: A dendrite method for cluster analysis publication-title: Comm. Statist. Theory Methods doi: 10.1080/03610927408827101 – volume: 5 start-page: 273 year: 1973 ident: 10.1016/j.csda.2021.107190_b38 article-title: A formalization of cluster analysis publication-title: Pattern Recognit. doi: 10.1016/0031-3203(73)90048-4 – volume: 17 start-page: 471 year: 2015 ident: 10.1016/j.csda.2021.107190_b23 article-title: Single cell rna-sequencing of pluripotent states unlocks modular transcriptional variation publication-title: Cell Stem Cell doi: 10.1016/j.stem.2015.09.011 – year: 2017 ident: 10.1016/j.csda.2021.107190_b27 – volume: 29 start-page: 965 year: 2004 ident: 10.1016/j.csda.2021.107190_b28 article-title: Species boundaries and phylogeographic patterns in cryptic taxa inferred from aflp markers: Veronica subgen. pentasepalae (scrophulariaceae) in the western mediterranean publication-title: Syst. Biol. – volume: 64 start-page: 53 year: 2015 ident: 10.1016/j.csda.2021.107190_b15 article-title: What are the true clusters? publication-title: Pattern Recognit. Lett. doi: 10.1016/j.patrec.2015.04.009 – year: 1987 ident: 10.1016/j.csda.2021.107190_b20 – year: 2015 ident: 10.1016/j.csda.2021.107190_b17 – volume: 11 start-page: 1 year: 2004 ident: 10.1016/j.csda.2021.107190_b41 article-title: Kernlab – an s4 package for kernel methods in r publication-title: J. Stat. Softw. – volume: 20 issue: 1131 year: 2013 ident: 10.1016/j.csda.2021.107190_b39 article-title: Single-cell rna-seq profiling of human preimplantation embryos and embryonic stem cells publication-title: Nat. Struct. Mol. Biol. – volume: 13 start-page: 221 year: 2013 ident: 10.1016/j.csda.2021.107190_b7 article-title: Classifying clustering schemes publication-title: Found. Comput. Math. doi: 10.1007/s10208-012-9141-9 – volume: 58 start-page: 91 year: 1971 ident: 10.1016/j.csda.2021.107190_b9 article-title: Admissible clustering procedures publication-title: Biometrika doi: 10.1093/biomet/58.1.91 – start-page: 121 year: 2009 ident: 10.1016/j.csda.2021.107190_b1 article-title: Measures of clustering quality: A working set of axioms for clustering – year: 1990 ident: 10.1016/j.csda.2021.107190_b21 – volume: 38 start-page: 1409 year: 1958 ident: 10.1016/j.csda.2021.107190_b34 article-title: A statistical method for evaluating systematic relationships publication-title: Univ. Kansas Sci. Bull. – volume: 24 start-page: 1787 year: 2014 ident: 10.1016/j.csda.2021.107190_b5 article-title: Cell fate inclination within 2-cell and 4-cell mouse embryos revealed by single-cell rna sequencing publication-title: Genome Res. doi: 10.1101/gr.177725.114 – start-page: 5 year: 2016 ident: 10.1016/j.csda.2021.107190_b26 – volume: 105 start-page: 199 year: 1993 ident: 10.1016/j.csda.2021.107190_b33 article-title: Multivariate data analysis in palaeoecology and palaeobiogeography-a review publication-title: Palaeogeogr. Palaeoclimatol. Palaeoecol. doi: 10.1016/0031-0182(93)90084-V – volume: 46 start-page: 243 year: 2012 ident: 10.1016/j.csda.2021.107190_b2 article-title: An extensive comparative study of cluster validity indices publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2012.07.021 – volume: 99 start-page: 1154 year: 2008 ident: 10.1016/j.csda.2021.107190_b14 article-title: Dissolution point and isolation robustness: robustness criteria for general cluster analysis methods publication-title: J. Multivariate Anal. doi: 10.1016/j.jmva.2007.07.002 – start-page: 463 year: 2003 ident: 10.1016/j.csda.2021.107190_b22 article-title: An impossibility theorem for clustering |
| SSID | ssj0002478 |
| Score | 2.5996132 |
| Snippet | The Average Silhouette Width (ASW) is a popular cluster validation index to estimate the number of clusters. The question whether it also is suitable as a... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 107190 |
| SubjectTerms | algorithms Axiomatic clustering data analysis data collection Distance-based clustering Number of clusters objectives Partitioning around medoids statistics |
| Title | Clustering with the Average Silhouette Width |
| URI | https://dx.doi.org/10.1016/j.csda.2021.107190 https://www.proquest.com/docview/2636448566 |
| Volume | 158 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NT8IwFG8IXvRg_Iz4QWbiTSdu61p6JESCEjiIBG7N1nZhhAwi29W_3ff2gdEYDp6adu2yvL6-j-7XXwm5C1yujYs77tyBBIWqwA6E4piqMM8IGJVD_ocj1p_Q15k_q5FudRYGYZWl7S9sem6ty5ZWKc3WOo5bYwTQC8rxEAp6GuQEpZSjlj9-fsM8XFpYY-T3xt7lwZkC46U2GrmHXAcauIN2-W_n9MtM576nd0QOy6DR6hTfdUxqJjkhB8Mt4-rmlDx0lxlyHoAnsnBv1YJnVgf0FOyFNY6X81WGoB5rGut0fkYmvef3bt8ub0Kwlcd5agcqdHTgCMOhGglIO6hRWrAICxbyp0gIX-G-oGJc6cgPQ6MdwbVwXRVBxHRO6skqMRfEgvVolBeGvkDimci0dZsFEMNxRb0281iDOJUIpCppwvG2iqWs8GALiWKTKDZZiK1B7rdj1gVJxs7efiVZ-WOqJVjxneNuq2mQsAbwx0aQmFW2kaBWmGZCZHr5z3dfkX2sFRiwa1JPPzJzA9FGGjZzdWqSvc7LoD_CcvA2HXwBiSXTSQ |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1NT8IwGG4IHtSD8TPi50z0pIjbupUePBCUgHxcgMitbm0XZsggwmK8-Kf8g74v2zAaw8HE07J2XZan7fvRPX1KyLlnMaUtXHFnJiQoVHpFj0uGqYpraw6t5pT_dset9-nDwBnkyEe2FwZplantT2z63FqnJaUUzdIkDEtdJNBzynATCnoamjIrm_rtFfK26W3jDjr5wrJq971qvZgeLVCUNmOzoid9U3km1wxuAw5xPNVScTfAi-uzm4BzR-JCm3SZVIHj-1qZnCluWTKgqHYAdn-FgrnAYxOu3794JRZNzD8KiuPnpTt1ElKZnCoUO7JMKGAmOoLfveEPvzB3drVNspFGqUYlAWKL5HS0TdbbC4nX6Q65qo5iFFkA12fgYq4BdUYFJgYYKKMbjobjGFlExmOoZsNd0v8XfPZIPhpHep8YYAC0tH3f4ah0E-iyKrseBI1MUrvs2m6BmBkEQqa65Hg8xkhkBLRngbAJhE0ksBXI5aLNJFHlWPq0kyErvo0tAW5jabuzrBsETDr8k-JFehxPBYxjzGshFD7447tPyWq9126JVqPTPCRrWJMQ0I5IfvYS62MIdWb-yXxoGeTpv8fyJ_DEDus |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Clustering+with+the+Average+Silhouette+Width&rft.jtitle=Computational+statistics+%26+data+analysis&rft.au=Batool%2C+Fatima&rft.au=Hennig%2C+Christian&rft.date=2021-06-01&rft.issn=0167-9473&rft.volume=158+p.107190-&rft_id=info:doi/10.1016%2Fj.csda.2021.107190&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-9473&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-9473&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-9473&client=summon |