Abstract
The self-organizing map is a kind of artificial neural network used to map high dimensional data into a low dimensional space. This chapter presents a self-organizing map to do unsupervised clustering for interval data. This map uses an extension of the Euclidian distance to compute the proximity between two vectors of intervals where each neuron represents a cluster. The performance of this approach is then illustrated and discussed while applied to temperature interval data coming from Chinese meteorological stations. The bounds of each interval are the measured minimal and maximal values of the temperature. In the presented experiments, stations of similar climate regions are assigned to the same neuron or to a neighbor neuron on the map.
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References
Cazes, P., Chouakria, A., Diday, E., Schektman, Y.: Extension de l’analyse en composantes principales à des données de type intervalle. Rev. Stat. Appl. 14, 5–24 (1997)
Chouakria, A.: Extension des méthodes d’analyse factorielle à des données de type intervalle. PhD dissertation, Université Paris-Dauphine (1998)
Billard, L., Diday, E.: Regression analysis for interval-valued data. In: Kiers, H., Rasson, J.-P., Groenen, P., Schader, M. (eds.) Data Analysis, Classification, and Related Methods, Proceedings of 7th Conference of the International Federation of Classification Societies (IFCS 2000), pp. 369–374. Springer, Heidelberg (2000)
Rossi, F., Conan-Guez, B.: Multi-layer perceptron on interval data. In: Jajuga, K., Sokolowski, A., Bock, H.-H. (eds.) Classification, Clustering, and Data Analysis, pp. 427–436. Springer, Berlin (2002)
Chavent, M., Lechevallier, Y.: Dynamical clustering of interval data: optimization of an adequacy criterion based on Hausdorff distance. In: Jajuga, K., Sokolowski, A., Bock, H.-H. (eds.) Classification, Clustering, and Data Analysis, pp. 53–60. Springer, Berlin (2002)
Barnsley, M.: Fractals everywhere, 2nd edn. Academic Press (1993)
Chavent, M.: Analyse des données symboliques. Une méthode divisive de classifi-cation. PhD dissertation, Université Paris-Dauphine (1997)
Bock, H.-H.: Clustering methods and Kohonen maps for symbolic data. J. Jpn. Soc. Comput. Stat. 15, 217–229 (2003)
Hamdan, H., Govaert, G.: Classification de données de type intervalle via l’algorithme EM. In: Proceedings of XXXVeme Journées de Statistique (SFdS), Lyon, France, pp. 549–552 (2003)
Hamdan, H., Govaert, G.: Modélisation et classification de données imprécises. In: Proceedings of Premier Congrès International sur les Modélisations Numériques Appliquées (CIMNA 2003), Beyrouth, Liban, pp. 16–19 (2003)
Hamdan, H., Govaert, G.: Mixture model clustering of uncertain data. In: Proceeding of IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2005), Reno, Nevada, USA, pp. 879–884 (2005)
Hamdan, H., Govaert, G.: CEM algorithm for imprecise data. Application to flaw diagnosis using acoustic emission. In: Proceedings of IEEE International Conference on Systems, Man and Cybernetics (IEEE SMC 2004), The Hague, The Netherlands, pp. 4774–4779 (2004)
Hamdan, H., Govaert, G.: Int-EM-CEM algorithm for imprecise data. Comparison with the CEM algorithm using Monte Carlo simulations. In: Proceedings of IEEE International Conference on Cybernetics and Intelligent Systems (IEEE CIS 2004), pp. 410–415 (2004)
Chavent, M.: An Hausdorff distance between hyper-rectangles for clustering interval data. In: Banks, D., House, L., McMorris, F.-R., Arabie, P., Gaul, W. (eds.) Classification, Clustering, and Data Mining Applications, pp. 333–340. Springer, Heidelberg (2004)
De Souza, R.M.C.R., De Carvalho, F.A.T.: Clustering of interval data based on city-block distances. Pattern Recognit. Lett. 25, 353–365 (2004)
De Souza, R.M.C.R., De Carvalho, F.A.T., Tenrio, C.P., Lechevallier, Y.: Dynamic cluster methods for interval data based on Mahalanobis distances. In: Proceedings of 9th Conference of the International Federation of Classification Societies (IFCS 2004), pp. 351–360. Springer, Heidelberg (2004)
El Golli, A., Conan-Guez, B., Rossi, F.: Self-organizing maps and symbolic data. J. Symb. Data Anal. (JSDA) 2 (2004)
Kohonen, T.: Self organization and associative memory, 2nd edn. Springer, Heidelberg (1984)
Kohonen, T.: Self-organizing maps, 3rd edn. Springer, Heidelberg (2001)
De Carvalho, F.A.T., Brito, P., Bock, H.-H.: Dynamic clustering for interval data based on L2 distance. Comput. Stat. 21, 231–250 (2006)
Hajjar, C., Hamdan, H.: Self-organizing map based on L2 distance for interval-valued data. In: Proceedings of IEEE 6th International Symposium on Applied Computational Intelligence and Informatics (IEEE SACI 2011), Timisoara, Romania, pp. 317–322 (2011)
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Hajjar, C., Hamdan, H. (2012). Clustering of Interval Data Using Self-Organizing Maps – Application to Meteorological Data. In: Precup, RE., Kovács, S., Preitl, S., Petriu, E. (eds) Applied Computational Intelligence in Engineering and Information Technology. Topics in Intelligent Engineering and Informatics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28305-5_11
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DOI: https://doi.org/10.1007/978-3-642-28305-5_11
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