{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:18:39Z","timestamp":1777533519985,"version":"3.51.4"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,1,9]],"date-time":"2013-01-09T00:00:00Z","timestamp":1357689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2013,4]]},"DOI":"10.1007\/s10208-012-9141-9","type":"journal-article","created":{"date-parts":[[2013,1,8]],"date-time":"2013-01-08T22:51:39Z","timestamp":1357685499000},"page":"221-252","source":"Crossref","is-referenced-by-count":45,"title":["Classifying Clustering Schemes"],"prefix":"10.1007","volume":"13","author":[{"given":"Gunnar","family":"Carlsson","sequence":"first","affiliation":[]},{"given":"Facundo","family":"M\u00e9moli","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,1,9]]},"reference":[{"key":"9141_CR1","first-page":"270","volume-title":"COLT","author":"M. Ackerman","year":"2010","unstructured":"M. Ackerman, S. Ben-David, D. Loker, Characterization of linkage-based clustering, in COLT, ed. by A.T. Kalai, M. Mohri (Omnipress, Madison, 2010), pp.\u00a0270\u2013281."},{"key":"9141_CR2","first-page":"121","volume-title":"NIPS","author":"S. Ben-David","year":"2008","unstructured":"S. Ben-David, M. Ackerman, Measures of clustering quality: a working set of axioms for clustering, in NIPS, ed. by D. Koller, D. Schuurmans, Y. Bengio, L. Bottou (Curran Associates, Inc., San Francisco, 2008), pp.\u00a0121\u2013128."},{"key":"9141_CR3","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1090\/S0273-0979-09-01249-X","volume":"46","author":"G. Carlsson","year":"2009","unstructured":"G. Carlsson, Topology and data, Bull. Am. Math. Soc. 46, 255\u2013308 (2009).","journal-title":"Bull. Am. Math. Soc."},{"issue":"4","key":"9141_CR4","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/s10208-010-9066-0","volume":"10","author":"G. Carlsson","year":"2010","unstructured":"G. Carlsson, V. de Silva, Zigzag persistence, Found. Comput. Math. 10(4), 367\u2013405 (2010).","journal-title":"Found. Comput. Math."},{"key":"9141_CR5","unstructured":"G. Carlsson, F. M\u00e9moli, Persistent clustering and a theorem of J.\u00a0Kleinberg. ArXiv e-prints, August 2008."},{"key":"9141_CR6","first-page":"1425","volume":"11","author":"G. Carlsson","year":"2010","unstructured":"G. Carlsson, F. M\u00e9moli, Characterization, stability and convergence of hierarchical clustering methods, J. Mach. Learn. Res. 11, 1425\u20131470 (2010).","journal-title":"J. Mach. Learn. Res."},{"key":"9141_CR7","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/978-3-642-10745-0_6","volume-title":"Classification as a Tool for Research","author":"G. Carlsson","year":"2010","unstructured":"G. Carlsson, F. M\u00e9moli, Multiparameter clustering methods, in Classification as a Tool for Research, ed. by C.W.H. Locarek-Junge. Proc. 11th Conference of the International Federation of Classification Societies (IFCS-09) (Springer, Heidelberg, 2010), pp.\u00a063\u201370."},{"key":"9141_CR8","first-page":"184","volume-title":"Symposium on Computational Geometry","author":"G. Carlsson","year":"2007","unstructured":"G. Carlsson, A. Zomorodian, The theory of multidimensional persistence, in Symposium on Computational Geometry (2007), pp.\u00a0184\u2013193."},{"key":"9141_CR9","first-page":"339","volume-title":"Algebraic and Geometric Topology","author":"V. Silva de","year":"2007","unstructured":"V. de Silva, R. Ghrist, Coverage in sensor networks via persistent homology, in Algebraic and Geometric Topology, vol.\u00a07 (2007) pp.\u00a0339\u2013358."},{"key":"9141_CR10","first-page":"226","volume-title":"A\u00a0Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise","author":"M. Ester","year":"1996","unstructured":"M. Ester, H.P. Kriegel, J. Sander, X. Xu, A\u00a0Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise (AAAI Press, Menlo Park, 1996), pp.\u00a0226\u2013231."},{"issue":"1","key":"9141_CR11","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1090\/S0273-0979-07-01191-3","volume":"45","author":"R. Ghrist","year":"2008","unstructured":"R. Ghrist, Barcodes: The persistent topology of data, Bull. Am. Math. Soc. 45(1), 61 (2008).","journal-title":"Bull. Am. Math. Soc."},{"key":"9141_CR12","unstructured":"R. Ghrist, Three examples of applied and computational homology, Lab Papers (GRASP), p.\u00a018 (2008)."},{"key":"9141_CR13","unstructured":"I. Guyon, U. von Luxburg, R. Williamson, Clustering: Science or art? Technical report, Paper presented at the NIPS 2009 Workshop Clustering: science or Art? http:\/\/www.kyb.tuebingen.mpg.de\/bs\/people\/ule\/publications\/publication_downloads\/IsClusteringScience.pdf (2009)."},{"key":"9141_CR14","series-title":"Ann. of Math. Stud.","first-page":"175","volume-title":"Prospects in Topology","author":"J.C. Hausmann","year":"1995","unstructured":"J.C. Hausmann, On the Vietoris-Rips complexes and a cohomology theory for metric spaces, in Prospects in Topology. Princeton, NJ, 1994, Ann. of Math. Stud., vol.\u00a0138 (Princeton Univ. Press, Princeton, 1995), pp.\u00a0175\u2013188."},{"key":"9141_CR15","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF02566944","volume":"39","author":"J.R. Isbell","year":"1964","unstructured":"J.R. Isbell, Six theorems about injective metric spaces, Comment. Math. Helv. 39, 65\u201376 (1964).","journal-title":"Comment. Math. Helv."},{"key":"9141_CR16","series-title":"Prentice Hall Advanced Reference Series","volume-title":"Algorithms for Clustering Data","author":"A.K. Jain","year":"1988","unstructured":"A.K. Jain, R.C. Dubes, Algorithms for Clustering Data. Prentice Hall Advanced Reference Series (Prentice Hall, Englewood Cliffs, 1988)."},{"key":"9141_CR17","series-title":"Wiley Series in Probability and Mathematical Statistics","volume-title":"Mathematical Taxonomy","author":"N. Jardine","year":"1971","unstructured":"N. Jardine, R. Sibson, Mathematical Taxonomy. Wiley Series in Probability and Mathematical Statistics (Wiley, London, 1971)."},{"key":"9141_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71962-5","volume-title":"Combinatorial Algebraic Topology","author":"D. Kozlov","year":"2008","unstructured":"D. Kozlov, D.N. Kozlov, Combinatorial Algebraic Topology (Springer, Berlin, 2008)."},{"key":"9141_CR19","first-page":"446","volume-title":"NIPS","author":"J.M. Kleinberg","year":"2002","unstructured":"J.M. Kleinberg, An impossibility theorem for clustering, in NIPS, ed. by S. Becker, S. Thrun, K. Obermayer (MIT Press, Cambridge, 2002), pp.\u00a0446\u2013453."},{"issue":"4","key":"9141_CR20","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1093\/comjnl\/9.4.373","volume":"9","author":"G.N. Lance","year":"1967","unstructured":"G.N. Lance, W.T. Williams, A\u00a0general theory of classificatory sorting strategies 1.\u00a0Hierarchical systems, Comput. J. 9(4), 373\u2013380 (1967).","journal-title":"Comput. J."},{"key":"9141_CR21","series-title":"Graduate Texts in Mathematics","volume-title":"Categories for the Working Mathematician","author":"S.M. Lane","year":"1998","unstructured":"S.M. Lane, Categories for the Working Mathematician, 2nd edn. Graduate Texts in Mathematics, vol.\u00a05 (Springer, New York, 1998).","edition":"2"},{"key":"9141_CR22","volume-title":"Topology: A First Course","author":"J.R. Munkres","year":"1975","unstructured":"J.R. Munkres, Topology: A First Course (Prentice Hall, Englewood Cliffs, 1975)."},{"key":"9141_CR23","doi-asserted-by":"crossref","DOI":"10.1002\/9780470175668","volume-title":"Handbook of Applied Algorithms: Solving Scientific, Engineering, and Practical Problems","author":"A. Nayak","year":"2008","unstructured":"A. Nayak, I. Stojmenovic, Handbook of Applied Algorithms: Solving Scientific, Engineering, and Practical Problems (Wiley\/IEEE Press, New York, 2008)."},{"issue":"7043","key":"9141_CR24","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1038\/nature03607","volume":"435","author":"G. Palla","year":"2005","unstructured":"G. Palla, I. Derenyi, I. Farkas, T. Vicsek, Uncovering the overlapping community structure of complex networks in nature and society, Nature 435(7043), 814\u2013818 (2005).","journal-title":"Nature"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-012-9141-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-012-9141-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-012-9141-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T07:05:12Z","timestamp":1559113512000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-012-9141-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,9]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,4]]}},"alternative-id":["9141"],"URL":"https:\/\/doi.org\/10.1007\/s10208-012-9141-9","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,9]]}}}