{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T03:59:44Z","timestamp":1768881584398,"version":"3.49.0"},"publisher-location":"Berlin, Heidelberg","reference-count":45,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662485767","type":"print"},{"value":"9783662485774","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-662-48577-4_4","type":"book-chapter","created":{"date-parts":[[2015,11,24]],"date-time":"2015-11-24T15:06:05Z","timestamp":1448377565000},"page":"50-71","source":"Crossref","is-referenced-by-count":2,"title":["Comparing Fuzzy Clusterings in High Dimensionality"],"prefix":"10.1007","author":[{"given":"Stefano","family":"Rovetta","sequence":"first","affiliation":[]},{"given":"Francesco","family":"Masulli","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,25]]},"reference":[{"issue":"5","key":"4_CR1","doi-asserted-by":"publisher","first-page":"906","DOI":"10.1109\/TFUZZ.2010.2052258","volume":"18","author":"DT Anderson","year":"2010","unstructured":"Anderson, D.T., Bezdek, J.C., Popescu, M., Keller, J.M.: Comparing fuzzy, probabilistic, and possibilistic partitions. IEEE Trans. Fuzzy Syst. 18(5), 906\u2013918 (2010)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"2","key":"4_CR2","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1109\/72.750571","volume":"10","author":"D Anguita","year":"1999","unstructured":"Anguita, D., Ridella, S., Rovetta, S.: Worst case analysis of weight inaccuracy effects in multilayer perceptrons. IEEE Trans. Neural Networks 10(2), 415\u2013418 (1999)","journal-title":"IEEE Trans. Neural Networks"},{"issue":"3","key":"4_CR3","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1109\/91.531780","volume":"4","author":"M Barni","year":"1996","unstructured":"Barni, M., Cappellini, V., Mecocci, A.: Comments on \u2018A possibilistic approach to clustering\u2019. IEEE Trans. Fuzzy Syst. 4(3), 393\u2013396 (1996)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"3","key":"4_CR4","first-page":"251","volume":"25","author":"C Baroni-Urbani","year":"1976","unstructured":"Baroni-Urbani, C., Buser, M.W.: Similarity of binary data. Syst. Biol. 25(3), 251\u2013259 (1976). http:\/\/sysbio.oxfordjournals.org\/content\/25\/3\/251.abstract","journal-title":"Syst. Biol."},{"key":"4_CR5","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/11776420_4","volume-title":"Learning Theory","author":"S Ben-David","year":"2006","unstructured":"Ben-David, S., von Luxburg, U., P\u00e1l, D.: A sober look at clustering stability. In: Lugosi, G., Simon, H.U. (eds.) COLT 2006. LNCS (LNAI), vol. 4005, pp. 5\u201319. Springer, Heidelberg (2006)"},{"key":"4_CR6","doi-asserted-by":"crossref","unstructured":"Ben-Hur, A., Elisseeff, A., Guyon, I.: A stability based method for discovering structure in clustered data. In: Altman, R.B., Dunker, A.K., Hunter, L., Lauderdale, K., Klein, T.E. (eds.) BIOCOMPUTING 2002 Proceedings of the Pacific Symposium, pp. 6\u201317 (2001)","DOI":"10.1142\/9789812799623_0002"},{"key":"4_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-0450-1","volume-title":"Pattern Recognition with Fuzzy Objective Function Algorithms","author":"JC Bezdek","year":"1981","unstructured":"Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers, Norwell (1981)"},{"issue":"3","key":"4_CR8","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/s10844-008-0054-7","volume":"32","author":"RK Brouwer","year":"2009","unstructured":"Brouwer, R.K.: Extending the rand, adjusted rand and jaccard indices to fuzzy partitions. J. Intell. Inf. Syst. 32(3), 213\u2013235 (2009)","journal-title":"J. Intell. Inf. Syst."},{"issue":"2","key":"4_CR9","doi-asserted-by":"publisher","first-page":"351","DOI":"10.2307\/2530449","volume":"38","author":"MW Buser","year":"1982","unstructured":"Buser, M.W., Baroni-Urbani, C.: A direct nondimensional clustering method for binary data. Biometrics 38(2), 351\u2013360 (1982). http:\/\/www.jstor.org\/stable\/2530449","journal-title":"Biometrics"},{"key":"4_CR10","doi-asserted-by":"publisher","first-page":"966","DOI":"10.1016\/j.patrec.2010.01.002","volume":"31","author":"RJGB Campello","year":"2010","unstructured":"Campello, R.J.G.B.: Generalized external indexes for comparing data partitions with overlapping categories. Pattern Recogn. Lett. 31, 966\u2013975 (2010)","journal-title":"Pattern Recogn. Lett."},{"issue":"12","key":"4_CR11","doi-asserted-by":"publisher","first-page":"2315","DOI":"10.1109\/TPAMI.2012.80","volume":"34","author":"C Carpineto","year":"2012","unstructured":"Carpineto, C., Romano, G.: Consensus clustering based on a new probabilistic rand index with application to subtopic retrieval. IEEE Trans. Pattern Anal. Mach. Intell. 34(12), 2315\u20132326 (2012)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"4_CR12","first-page":"43","volume":"8","author":"SS Choi","year":"2010","unstructured":"Choi, S.S., Cha, S.H., Tappert, C.C.: A survey of binary similarity and distance measures. J. Systemics Cybern. Inf. 8, 43\u201348 (2010)","journal-title":"J. Systemics Cybern. Inf."},{"issue":"3","key":"4_CR13","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1145\/29380.29864","volume":"13","author":"A Corana","year":"1987","unstructured":"Corana, A., Marchesi, M., Martini, C., Ridella, S.: Minimizing multimodal functions of continuous variables with the \u201csimulated annealing\u201d algorithm. ACM Trans. Math. Softw. 13(3), 262\u2013280 (1987)","journal-title":"ACM Trans. Math. Softw."},{"issue":"2","key":"4_CR14","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1109\/91.580801","volume":"5","author":"RN Dav\u00e9","year":"1997","unstructured":"Dav\u00e9, R.N., Krishnapuram, R.: Robust clustering methods: a unified view. IEEE Trans. Fuzzy Syst. 5(2), 270\u2013293 (1997)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"4_CR15","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1109\/TFUZZ.2010.2043440","volume":"18","author":"M Filippone","year":"2010","unstructured":"Filippone, M., Masulli, F., Rovetta, S.: Applying the possibilistic c-means algorithm in kernel-induced spaces. IEEE Trans. Fuzzy Syst. 18, 572\u2013584 (2010)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"383","key":"4_CR16","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1080\/01621459.1983.10478008","volume":"78","author":"EB Fowlkes","year":"1983","unstructured":"Fowlkes, E.B., Mallows, C.L.: A method for comparing two hierarchical clusterings. J. Am. Stat. Assoc. 78(383), 553\u2013569 (1983). http:\/\/dx.doi.org\/10.2307\/2288117","journal-title":"J. Am. Stat. Assoc."},{"key":"4_CR17","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1109\/ICPR.2002.1047450","volume":"4","author":"ALN Fred","year":"2002","unstructured":"Fred, A.L.N., Jain, A.K.: Data clustering using evidence accumulation. Int. Conf. Pattern Recog. 4, 276\u2013280 (2002)","journal-title":"Int. Conf. Pattern Recog."},{"issue":"5","key":"4_CR18","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1109\/34.765656","volume":"21","author":"H Frigui","year":"1999","unstructured":"Frigui, H., Krishnapuram, R.: A robust competitive clustering algorithm with applications in computer vision. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 450\u2013465 (1999)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"4_CR19","unstructured":"Frigui, H., Krishnapuram, R.: A robust clustering algorithm based on m-estimator. In: Proceedings of the 1st International Conference on Neural, Parallel and Scientific Computations, Atlanta, USA, vol. 1, pp. 163\u2013166, May 1995"},{"key":"4_CR20","doi-asserted-by":"publisher","DOI":"10.1002\/0471725250","volume-title":"Robust Stat.","author":"PJ Huber","year":"1981","unstructured":"Huber, P.J.: Robust Stat. Wiley, New York (1981)"},{"issue":"1","key":"4_CR21","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/BF01908075","volume":"2","author":"L Hubert","year":"1985","unstructured":"Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193\u2013218 (1985)","journal-title":"J. Classif."},{"key":"4_CR22","first-page":"547","volume":"37","author":"P Jaccard","year":"1901","unstructured":"Jaccard, P.: \u00c9tude comparative de la distribution florale dans une portion des alpes et des jura. Bull. Soc. Vaudoise des Sci. Nat. 37, 547\u2013579 (1901)","journal-title":"Bull. Soc. Vaudoise des Sci. Nat."},{"issue":"3","key":"4_CR23","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1016\/S0022-0000(05)80062-5","volume":"48","author":"M Kearns","year":"1994","unstructured":"Kearns, M., Schapire, R.: Efficient distribution-free learning of probabilistic concepts. J. Comput. Syst. Sci. 48(3), 464\u2013497 (1994)","journal-title":"J. Comput. Syst. Sci."},{"issue":"3","key":"4_CR24","first-page":"125","volume":"11","author":"F Klawonn","year":"2004","unstructured":"Klawonn, F.: Fuzzy clustering: insights and a new approach. Mathware Soft Comput. 11(3), 125\u2013142 (2004)","journal-title":"Mathware Soft Comput."},{"issue":"2","key":"4_CR25","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1109\/91.227387","volume":"1","author":"R Krishnapuram","year":"1993","unstructured":"Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1(2), 98\u2013110 (1993)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"3","key":"4_CR26","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1109\/91.531779","volume":"4","author":"R Krishnapuram","year":"1996","unstructured":"Krishnapuram, R., Keller, J.M.: The possibilistic $$C$$ C -Means algorithm: insights and recommendations. IEEE Trans. Fuzzy Syst. 4(3), 385\u2013393 (1996)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"11","key":"4_CR27","doi-asserted-by":"publisher","first-page":"1798","DOI":"10.1109\/TPAMI.2006.226","volume":"28","author":"LI Kuncheva","year":"2006","unstructured":"Kuncheva, L.I., Vetrov, D.P.: Evaluation of stability of k-means cluster ensembles with respect to random initialization. IEEE Trans. Pattern Anal. Mach. Intell. 28(11), 1798\u20131808 (2006)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"6","key":"4_CR28","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1162\/089976604773717621","volume":"16","author":"T Lange","year":"2004","unstructured":"Lange, T., Roth, V., Braun, M.L., Buhmann, J.M.: Stability-based validation of clustering solutions. Neural Comput. 16(6), 1299\u20131323 (2004)","journal-title":"Neural Comput."},{"key":"4_CR29","doi-asserted-by":"crossref","unstructured":"Masulli, F., Rovetta, S.: Clustering High-Dimensional Data. In: Proceedings of CHDD 2012, Clustering High-Dimensional Data, Series Lecture Notes in Computer Science, LNCS 7627, 1, Springer-Verlag, Heidelberg, Germany (2015)","DOI":"10.1007\/978-3-662-48577-4_1"},{"issue":"4","key":"4_CR30","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1109\/TFUZZ.2006.876740","volume":"14","author":"F Masulli","year":"2006","unstructured":"Masulli, F., Rovetta, S.: Soft transition from probabilistic to possibilistic fuzzy clustering. IEEE Trans. Fuzzy Syst. 14(4), 516\u2013527 (2006)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"5","key":"4_CR31","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1016\/j.jmva.2006.11.013","volume":"98","author":"M Meil\u0103","year":"2007","unstructured":"Meil\u0103, M.: Comparing clusterings-an information based distance. J. Multivar. Anal. 98(5), 873\u2013895 (2007). http:\/\/dx.doi.org\/10.1016\/j.jmva.2006.11.013","journal-title":"J. Multivar. Anal."},{"issue":"6","key":"4_CR32","doi-asserted-by":"publisher","first-page":"1325","DOI":"10.1016\/S0031-3203(02)00049-3","volume":"36","author":"M M\u00e9nard","year":"2003","unstructured":"M\u00e9nard, M., Courboulay, V., Dardignac, P.A.: Possibilistic and probabilistic fuzzy clustering: unification within the framework of the non-extensive thermostatistics. Pattern Recogn. 36(6), 1325\u20131342 (2003)","journal-title":"Pattern Recogn."},{"issue":"12","key":"4_CR33","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1073\/pnas.28.12.535","volume":"28","author":"K Menger","year":"1942","unstructured":"Menger, K.: Statistical metrics. Proc. Natl. Acad. Sci. U.S.A. 28(12), 535\u2013537 (1942)","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"4_CR34","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717716","volume-title":"Introduction to Interval Analysis","author":"RE Moore","year":"2009","unstructured":"Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. Society for Industrial Mathematics, Philadelphia (2009)"},{"key":"4_CR35","doi-asserted-by":"crossref","unstructured":"Pal, N.R., Pal, K., Bezdek, J.C.: A mixed c-Means clustering model. In: FUZZIEEE97: Proceedings of the International Conference on Fuzzy Systems, pp. 11\u201321. IEEE, Barcelona (1997)","DOI":"10.1109\/FUZZY.1997.616338"},{"key":"4_CR36","doi-asserted-by":"publisher","first-page":"846","DOI":"10.1080\/01621459.1971.10482356","volume":"66","author":"W Rand","year":"1971","unstructured":"Rand, W.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66, 846\u2013850 (1971)","journal-title":"J. Am. Stat. Assoc."},{"key":"4_CR37","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1093\/sysbio\/45.3.380","volume":"45","author":"R Real","year":"1996","unstructured":"Real, R., Vargas, J.M.: The probabilistic basis of jaccard\u2019s index of similarity. Syst. Biol. 45, 380\u2013385 (1996)","journal-title":"Syst. Biol."},{"key":"4_CR38","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/0167-8655(90)90010-Y","volume":"11","author":"K Rose","year":"1990","unstructured":"Rose, K., Gurewitz, E., Fox, G.: A deterministic annealing approach to clustering. Pattern Recogn. Lett. 11, 589\u2013594 (1990)","journal-title":"Pattern Recogn. Lett."},{"key":"4_CR39","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1103\/PhysRevLett.65.945","volume":"65","author":"K Rose","year":"1990","unstructured":"Rose, K., Gurewitz, E., Fox, G.: Statistical mechanics and phase transitions in clustering. Phys. Rev. Lett. 65, 945\u2013948 (1990)","journal-title":"Phys. Rev. Lett."},{"key":"4_CR40","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1007\/978-3-642-02282-1_17","volume-title":"Fuzzy Logic and Applications","author":"S Rovetta","year":"2009","unstructured":"Rovetta, S., Masulli, F.: An experimental validation of some indexes of fuzzy clustering similarity. In: Di Ges\u00f9, V., Pal, S.K., Petrosino, A. (eds.) WILF 2009. LNCS, vol. 5571, pp. 132\u2013139. Springer, Heidelberg (2009)"},{"key":"4_CR41","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.ins.2014.01.031","volume":"279","author":"S Rovetta","year":"2014","unstructured":"Rovetta, S., Masulli, F.: Visual stability analysis for model selection in graded possibilistic clustering. Inf. Sci. 279, 37\u201351 (2014)","journal-title":"Inf. Sci."},{"issue":"1","key":"4_CR42","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/S0019-9958(69)90591-9","volume":"15","author":"EH Ruspini","year":"1969","unstructured":"Ruspini, E.H.: A new approach to clustering. Inf. Control 15(1), 22\u201332 (1969)","journal-title":"Inf. Control"},{"issue":"3\u20134","key":"4_CR43","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0031-0182(93)90084-V","volume":"105","author":"G Shi","year":"1993","unstructured":"Shi, G.: Multivariate data analysis in palaeoecology and palaeobiogeographya review. Palaeogeogr. Palaeoclimatol. Palaeoecol. 105(3\u20134), 199\u2013234 (1993)","journal-title":"Palaeogeogr. Palaeoclimatol. Palaeoecol."},{"issue":"2","key":"4_CR44","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1111\/1467-9868.00293","volume":"63","author":"R Tibshirani","year":"2001","unstructured":"Tibshirani, R., Walther, G., Hastie, T.: Estimating the number of clusters in a data set via the gap statistic. J. Roy. Stat. Soc. Ser. B Stat. Methodol. 63(2), 411\u2013423 (2001). http:\/\/dx.doi.org\/10.1111\/1467-9868.00293","journal-title":"J. Roy. Stat. Soc. Ser. B Stat. Methodol."},{"issue":"3","key":"4_CR45","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338\u2013353 (1965)","journal-title":"Inf. Control"}],"container-title":["Lecture Notes in Computer Science","Clustering High--Dimensional Data"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-48577-4_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,31]],"date-time":"2025-05-31T14:05:58Z","timestamp":1748700358000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-48577-4_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783662485767","9783662485774"],"references-count":45,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-48577-4_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}