Geodesic
Cluster networks and Bruhat–Tits buildings
Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 2, pp. 234-244 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a clustering procedure in the case where a family of metrics is used instead of a fixed metric. In this case, a classification network (a directed acyclic graph with nondirected cycles) is obtained instead of a classification tree. We discuss the relation to Bruhat–Tits buildings and introduce the notion of the dimension of a general cluster network.
Keywords: clustering, cluster network, Bruhat–Tits building. 
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S. V. Kozyrev. Cluster networks and Bruhat–Tits buildings. Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 2, pp. 234-244. http://geodesic.mathdoc.fr/item/TMF_2014_180_2_a5/

[1] S. Albeverio, S. V. Kozyrev, $p$-Adic Numbers Ultrametric Anal. Appl., 4:3 (2012), 167–178, arXiv: 1204.5952 | DOI | MR | Zbl

[2] S. V. Kozyrev, TMF, 164:3 (2010), 394–400 | DOI | DOI | Zbl

[3] J. Benois-Pineau, A. Khrennikov, Computer J., 53:4 (2010), 417–431 | DOI

[4] Zh. Benua-Pino, A. Yu. Khrennikov, N. Kotovich, Dokl. RAN, 381:5 (2001), 604–609 | MR

[5] F. Murtagh, Multidimensional Clustering Algorithms, Physica-Verlag, Heidelberg, 1985 | MR | Zbl

[6] P. B. Garrett, Buildings and Classical Groups, Chapman and Hall, London, 1997 | MR | Zbl

[7] A. Veil, Osnovy teorii chisel, Mir, M., 1972 | MR

[8] V. N. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995 | MR | Zbl

[9] E. V. Kunin, Logika sluchaya. O prirode i proiskhozhdenii biologicheskoi evolyutsii, Tsentrpoligraf, M., 2014

[10] D. H. Huson, R. Rupp, C. Scornavacca, Phylogenetic Networks, Cambridge Univ. Press, Cambridge, 2010

[11] A. Dress, K. T. Huber, J. Koolen, V. Moulton, A. Spillner, Basic Phylogenetic Combinatorics, Cambridge Univ. Press, Cambridge, 2012 | MR | Zbl