An Order Theoretic Model for Cluster Analysis
To effectively deal with ordinal clustering problems, an order theoretic model for the subject is presented. It is compared to an earlier graph theoretic model due to N. Jardine and R. Sibson. Some of its salient properties are established, with special attention paid to the incorporation of Jardine...
Saved in:
| Published in | SIAM journal on applied mathematics Vol. 34; no. 1; pp. 55 - 72 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.1978
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0036-1399 1095-712X |
| DOI | 10.1137/0134005 |
Cover
| Abstract | To effectively deal with ordinal clustering problems, an order theoretic model for the subject is presented. It is compared to an earlier graph theoretic model due to N. Jardine and R. Sibson. Some of its salient properties are established, with special attention paid to the incorporation of Jardine and Sibson's "flat" cluster methods into the model. It is shown how the characterization of flat cluster methods leads to a universal mapping problem in the theory of partially ordered sets. This problem is solved, and its solution applied both to the present model and to the Jardine-Sibson model. |
|---|---|
| AbstractList | To effectively deal with ordinal clustering problems, an order theoretic model for the subject is presented. It is compared to an earlier graph theoretic model due to N. Jardine and R. Sibson. Some of its salient properties are established, with special attention paid to the incorporation of Jardine and Sibson's "flat" cluster methods into the model. It is shown how the characterization of flat cluster methods leads to a universal mapping problem in the theory of partially ordered sets. This problem is solved, and its solution applied both to the present model and to the Jardine-Sibson model. |
| Author | Janowitz, M. F. |
| Author_xml | – sequence: 1 givenname: M. F. surname: Janowitz fullname: Janowitz, M. F. |
| BookMark | eNpt0D1PwzAQBmALFYm2IP4AQ8TCZLizHccZq4ovqahLkdgi23FEqhAX2xn670nVigEx3XDPvTq9MzLpfe8IuUa4R-TFAyAXAPkZmSKUOS2QfUzIFIBLirwsL8gsxi0AohTllNBFn61D7UK2-XQ-uNTa7M3XrssaH7JlN8Q07ha97vaxjZfkvNFddFenOSfvT4-b5QtdrZ9fl4sVtQx4ooYJJUrkWlprFDhjJTKpalDcNkwLpqzJrS5YzmzZgHRGG8O4rbloJK8Nn5PbY-4u-O_BxVRt_RDGJ2JV4uFMFWJEd0dkg48xuKbahfZLh32FUB2qqE5VjJL-kbZNOrW-T0G33T_-5ui3MfnwG8sQQOUF_wGtqWhm |
| CitedBy_id | crossref_primary_10_1016_0166_218X_91_90021_N crossref_primary_10_1007_BF00565653 crossref_primary_10_1016_S0012_365X_98_00067_3 crossref_primary_10_1016_0165_4896_93_90001_Y crossref_primary_10_1016_0165_0114_88_90080_2 crossref_primary_10_1137_0605013 crossref_primary_10_1137_0137010 crossref_primary_10_1016_0166_218X_81_90035_4 crossref_primary_10_1007_BF01894188 crossref_primary_10_1006_eujc_1999_0379 crossref_primary_10_1016_S0165_4896_01_00081_6 crossref_primary_10_1137_060676532 crossref_primary_10_1016_S0166_218X_01_00354_7 crossref_primary_10_1016_0165_4896_91_90039_T crossref_primary_10_1016_0022_247X_86_90312_4 crossref_primary_10_1134_S2070046612010062 crossref_primary_10_1007_BF01195143 crossref_primary_10_1016_0022_2496_86_90020_9 crossref_primary_10_1007_BF01719499 crossref_primary_10_1016_0165_4896_90_90077_K crossref_primary_10_1016_j_dam_2007_05_024 crossref_primary_10_1137_0605048 crossref_primary_10_1016_0012_365X_78_90146_2 crossref_primary_10_1007_s00357_012_9106_3 crossref_primary_10_1134_S0081543809020175 crossref_primary_10_1016_0165_0114_91_90256_P crossref_primary_10_1007_s10479_007_0174_4 crossref_primary_10_1016_0022_247X_88_90119_9 crossref_primary_10_1016_0165_4896_84_90060_X crossref_primary_10_1016_0165_4896_93_90052_K crossref_primary_10_1016_0165_4896_93_90030_M crossref_primary_10_1007_BF01908077 crossref_primary_10_1007_BF00383176 crossref_primary_10_1016_S0166_218X_02_00206_8 crossref_primary_10_1016_0022_2496_79_90035_X crossref_primary_10_1016_0165_4896_89_90043_7 |
| Cites_doi | 10.1038/212218a0 10.1016/0012-365X(78)90146-2 10.2307/2344237 10.1126/science.176.4035.659-a 10.1176/ajp.133.2.150 10.1093/comjnl/9.4.373 10.1093/comjnl/11.2.177 10.1080/01621459.1967.10500923 10.3109/00365517609068022 10.1111/j.2517-6161.1972.tb00910.x 10.1093/comjnl/14.2.162 10.1093/comjnl/14.2.156 10.1016/0025-5564(68)90030-8 10.1139/b75-060 10.1139/b76-008 10.1016/0025-5564(70)90077-5 10.1093/biomet/58.1.91 |
| ContentType | Journal Article |
| Copyright | Copyright 1978 Society for Industrial and Applied Mathematics [Copyright] © 1978 © Society for Industrial and Applied Mathematics |
| Copyright_xml | – notice: Copyright 1978 Society for Industrial and Applied Mathematics – notice: [Copyright] © 1978 © Society for Industrial and Applied Mathematics |
| DBID | AAYXX CITATION 3V. 7RQ 7WY 7WZ 7X2 7XB 87Z 88A 88F 88I 88K 8AL 8FE 8FG 8FH 8FK 8FL 8G5 ABJCF ABUWG AFKRA ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI CCPQU D1I DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JQ2 K60 K6~ K7- KB. L.- L6V LK8 M0C M0K M0N M1Q M2O M2P M2T M7P M7S MBDVC P5Z P62 PATMY PDBOC PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS PYCSY Q9U U9A |
| DOI | 10.1137/0134005 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Career & Technical Education Database ABI/INFORM Collection ABI/INFORM Global (PDF only) Agricultural Science Collection ProQuest Central (purchase pre-March 2016) ABI/INFORM Global (Alumni Edition) Biology Database (Alumni Edition) Military Database (Alumni Edition) Science Database (Alumni Edition) Telecommunications (Alumni Edition) Computing Database (Alumni Edition) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Natural Science Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni) Research Library (Alumni) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection Agricultural & Environmental Science Collection ProQuest Central Essentials Biological Science Collection ProQuest Central Business Premium Collection Technology Collection Natural Science Collection ProQuest One Community College ProQuest Materials Science Collection ProQuest Central Korea Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student ProQuest Research Library SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database Materials Science Database ABI/INFORM Professional Advanced ProQuest Engineering Collection ProQuest Biological Science Collection ABI/INFORM Global Agricultural Science Database Computing Database Military Database Research Library Science Database Telecommunications Database Biological Science Database Engineering Database Research Library (Corporate) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Environmental Science Database Materials Science Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Business ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection Environmental Science Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Agricultural Science Database ProQuest Business Collection (Alumni Edition) Research Library Prep Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest Military Collection ProQuest Central China ABI/INFORM Complete ProQuest Telecommunications ProQuest One Applied & Life Sciences Natural Science Collection Biological Science Collection ProQuest Central (New) Engineering Collection Career and Technical Education (Alumni Edition) Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Biological Science Collection ProQuest One Academic Eastern Edition Agricultural Science Collection ProQuest Technology Collection ProQuest Telecommunications (Alumni Edition) Biological Science Database ProQuest Business Collection Environmental Science Collection ProQuest Career and Technical Education ProQuest One Academic UKI Edition Environmental Science Database ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection ProQuest One Academic Middle East (New) Materials Science Collection ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Natural Science Collection ProQuest Biology Journals (Alumni Edition) ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ProQuest Central Korea Agricultural & Environmental Science Collection Materials Science Database ProQuest Research Library ABI/INFORM Complete (Alumni Edition) ProQuest Materials Science Collection ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest Military Collection (Alumni Edition) ProQuest SciTech Collection Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) |
| DatabaseTitleList | Agricultural Science Database |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Geology Mathematics |
| EISSN | 1095-712X |
| EndPage | 72 |
| ExternalDocumentID | 2567913271 10_1137_0134005 2100857 |
| GroupedDBID | -DZ -~X 123 2AX 4.4 7RQ 7WY 7X2 7XC 85S 88I 8CJ 8FE 8FG 8FH 8FL 8G5 AALVN AAWIL ABAWQ ABBHK ABFAN ABJCF ABPFR ABPPZ ABPQH ABUWG ABXSQ ABYWD ACBEA ACGFO ACGOD ACHJO ACIWK ACMTB ACNCT ACPRK ACTMH ACUBG ADBBV ADODI ADULT AENEX AEUPB AFKRA AFRAH AFVYC AFXHP AGLNM AIHAF ALMA_UNASSIGNED_HOLDINGS ALRMG ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI BPHCQ CCPQU CS3 CZ9 D1I D1J D1K DQDLB DSRWC DU5 DWQXO EBS ECEWR EJD ESX F5P FEDTE FRNLG FVMVE GNUQQ GUQSH HCIFZ HGD HQ6 HVGLF IPSME JAAYA JAS JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JST K6- K60 K6V K6~ K7- KB. KC. L6V LK5 LK8 M0C M0K M1Q M2O M2P M7P M7R M7S MVM NHB P1Q P2P P62 PATMY PDBOC PHGZM PHGZT PQBIZ PQBZA PQQKQ PROAC PTHSS PYCSY RJG RNS RSI SA0 T9H TN5 VOH WH7 YNT YXE YYP ~02 .4S .DC 8WZ A6W AAYJJ AAYXX ABDBF ABKAD ABMZU ACUHS ANXRF ARCSS CITATION DQ2 EAP EDO EMK EST H13 H~9 I-F TAE TUS WHG XSW ZCG 3V. 7XB 88A 88K 8AL 8FK JQ2 L.- M0N M2T MBDVC PKEHL PQEST PQGLB PQUKI PRINS PUEGO Q9U U9A |
| ID | FETCH-LOGICAL-c203t-b2484913a6ccb80ebc61268d083cf2a428cb5ca7252c9f06ebabb23cd34f63db3 |
| IEDL.DBID | BENPR |
| ISSN | 0036-1399 |
| IngestDate | Mon Aug 25 14:15:11 EDT 2025 Thu Apr 24 23:05:39 EDT 2025 Tue Jul 01 02:35:29 EDT 2025 Thu Jun 19 15:13:35 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c203t-b2484913a6ccb80ebc61268d083cf2a428cb5ca7252c9f06ebabb23cd34f63db3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| PQID | 917252874 |
| PQPubID | 666314 |
| PageCount | 18 |
| ParticipantIDs | proquest_journals_917252874 crossref_primary_10_1137_0134005 crossref_citationtrail_10_1137_0134005 jstor_primary_2100857 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 1900 |
| PublicationDate | 19780101 1978-01-00 |
| PublicationDateYYYYMMDD | 1978-01-01 |
| PublicationDate_xml | – month: 1 year: 1978 text: 19780101 day: 1 |
| PublicationDecade | 1970 |
| PublicationPlace | Philadelphia |
| PublicationPlace_xml | – name: Philadelphia |
| PublicationTitle | SIAM journal on applied mathematics |
| PublicationYear | 1978 |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher_xml | – name: Society for Industrial and Applied Mathematics |
| References | Jardine N. (R12) 1973 King D. S. (R15) 1976; 54 Blyth T. S. (R1) 1972 Turner B. J. (R29) 1974; 20 Sibson Robin (R24) 1972; 34 Sneath P. H. A. (R25) 1976; 76 R23 R22 Hartigan John A. (R7) 1975 R27 Rohlf F. J. (R21) 1974; 69 Lerman I. C. (R19) 1970 Jardine N. (R11) 1971; 14 R2 R3 R4 R5 R6 R8 R9 Knecht G. R. (R16) 1975; 23 R30 R10 R14 R13 Sneath Peter H. A. (R26) 1973 Straach P. (R28) 1975; 21 R18 R17 |
| References_xml | – volume-title: Mathematical Taxonomy year: 1973 ident: R12 – volume: 76 start-page: 19 year: 1976 ident: R25 publication-title: Z. Pflanzenz. – ident: R17 doi: 10.1038/212218a0 – ident: R8 doi: 10.1016/0012-365X(78)90146-2 – ident: R3 doi: 10.2307/2344237 – ident: R4 doi: 10.1126/science.176.4035.659-a – ident: R13 doi: 10.1176/ajp.133.2.150 – ident: R18 doi: 10.1093/comjnl/9.4.373 – volume: 54 start-page: 1286 year: 1976 ident: R15 publication-title: Canad. J. Botany – volume: 23 year: 1975 ident: R16 publication-title: Operational Res. Quart. – volume-title: Les bases de la classification automatique year: 1970 ident: R19 – ident: R9 doi: 10.1093/comjnl/11.2.177 – volume: 14 start-page: 404 year: 1971 ident: R11 publication-title: Math. Biosci. – volume: 69 start-page: 705 year: 1974 ident: R21 publication-title: J. Amer. Statist. Assoc. – ident: R6 doi: 10.1080/01621459.1967.10500923 – ident: R27 doi: 10.3109/00365517609068022 – volume: 34 start-page: 311 year: 1972 ident: R24 publication-title: J. Roy. Statist. Soc. Ser. B doi: 10.1111/j.2517-6161.1972.tb00910.x – ident: R30 doi: 10.1093/comjnl/14.2.162 – volume-title: Residuation theory year: 1972 ident: R1 – ident: R23 doi: 10.1093/comjnl/14.2.156 – ident: R10 doi: 10.1016/0025-5564(68)90030-8 – volume: 20 start-page: 343 year: 1974 ident: R29 publication-title: Forest. Sci. – ident: R2 doi: 10.1139/b75-060 – volume: 21 start-page: 269 year: 1975 ident: R28 publication-title: Z. Angew. Geologie – ident: R14 doi: 10.1139/b76-008 – ident: R22 doi: 10.1016/0025-5564(70)90077-5 – ident: R5 doi: 10.1093/biomet/58.1.91 – volume-title: Clustering algorithms year: 1975 ident: R7 – volume-title: Numerical taxonomy year: 1973 ident: R26 |
| SSID | ssj0011649 |
| Score | 1.2867268 |
| Snippet | To effectively deal with ordinal clustering problems, an order theoretic model for the subject is presented. It is compared to an earlier graph theoretic model... |
| SourceID | proquest crossref jstor |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 55 |
| SubjectTerms | Axioms Classification Cluster analysis Equivalence relation Geology Homomorphisms Mathematical models Modeling Partially ordered sets Real numbers Topology |
| Title | An Order Theoretic Model for Cluster Analysis |
| URI | https://www.jstor.org/stable/2100857 https://www.proquest.com/docview/917252874 |
| Volume | 34 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1NTwIxEJ0gXPRg_MCIKOnBeNu42-7W9mAMEpCYgMZAwm3Trz0RQIH_73S_EkPiuT3NtNP3pu17APeRFZqLJAm8L1IQZ0hYFbIw3HiIFVyYWa58a2Ay5eN5_L5IFg2YVH9h_LPKqibmhdquje-RPyKtoIkXZ3_ZfAfeNMpfrlYOGqp0VrDPucLYEbSwIgtc9q3X4fTzq75WQG4gKxVehD6y-EUbRV7kJ2K4nJM_x1PxQvGgSudHz-gMTkvMSPpFks-h4VYXcDKpBVe3lxD0V-TDq2iSWfUzkXibsyVBUEoGy73XQyCVAkkb5qPhbDAOSieEwNCQ7QJNYxHLiClujBah0waBCRcW8ZPJqEIKYXRilI-QkVnInVZaU2YsizPOrGZX0FytV-4aSBhqIcPYINOiseJOGiOtkFlCHcbMiQ48VAFITSkT7t0qlmlOF9hTWkaqA6SeuCmUMQ6ntPMI1uM0yhX1O9CtIpqWW2ab1gm--Xe0C8dRrgrsuyC30Nz97N0d4oKd7sGRGL31ypz_AuootNk |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3LTgIxFL1BWKgL4wMj4qMLdTdxpvOwsyAGEQLy0BhI2I1tp7MiAwrE-HH-m7fzSoyJO9ZtZpLbxz2n7T0H4MoKmfCY6xraF8lwIiSsHFkYLjzECsqMQo_ro4HhyOtOnKepOy3Bd14Lo59V5ntislGHc6nPyG-RVlBXi7PfL94NbRqlL1dzBw2eOSuEjURhLKvr6KuvT2Rwy0bvEYf7mtJOe9zqGpnJgCGpaa8MQR3m-JbNPSkFM5WQmPM9FiI0kRHliM6lcCXXP5d-ZHpKcCGoLUPbiTw7FDZ-dwsqji5wLUPloT16eS2uMZCL-LnqL0ItP63atSwtKmTZuHzcX-kwfRH5Jyskqa6zD3sZRiXNdFIdQEnFh7A7LARel0dgNGPyrFU7yTivhCTaVm1GEAST1myt9RdIrnhShclGgnIM5XgeqxMgpimYbzoSmR11uKd8Kf2Q-ZFLFWZNxWpwkwcgkJksuXbHmAUJPbHvgixSNSBFx0WqxPG3SzWJYNFOrUTBvwb1PKJBtkSXQTGhTv9tvYTt7ng4CAa9Ub8OO1aiSKxPYM6gvPpYq3PEJCtxkY08gbdNT7Yf3gjx5g |
| 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=An+Order+Theoretic+Model+for+Cluster+Analysis&rft.jtitle=SIAM+journal+on+applied+mathematics&rft.au=Janowitz%2C+M.+F&rft.date=1978-01-01&rft.pub=Society+for+Industrial+and+Applied+Mathematics&rft.issn=0036-1399&rft.eissn=1095-712X&rft.volume=34&rft.issue=1&rft.spage=55&rft_id=info:doi/10.1137%2F0134005&rft.externalDocID=2567913271 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0036-1399&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0036-1399&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0036-1399&client=summon |