Abstract
Prototype based neural clustering or data mining methods such as the self-organizing map or neural gas constitute intuitive and powerful machine learning tools for a variety of application areas. However, the classical methods are restricted to data embedded in a real vector space and have only limited applicability to noneuclidean data as occurs in, for example, biomedical or symbolic fields. Recently, extensions of unsupervised neural prototype based clustering to dissimilarity data, i.e. data characterized in terms of a dissimilarity matrix only, have been proposed substituting the mean by the so-called generalized median. Thereby, the location of prototypes is chosen within the discrete input space which constitutes a severe limitation in particular for sparse data sets since the prototype flexibility is restricted. Here we present a generalization of median neural gas such that prototypes can be interpreted as mixtures of discrete input locations. We derive a batch optimization scheme based on a corresponding cost function.
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References
Barreto, G., Araujo, A., Kremer, S.: A taxonomy for spatiotemporal connectionist networks revisited: the unsupervised case. Neural Computation 15, 1255–1320 (2003)
Conan-Guez, B., Rossi, F., El Golli, A.: A fast algorithm for the self-organizing map on dissimilarity data. In: Workshop on Self-Organizing Maps, pp. 561–568 (2005)
Cottrell, M., Hammer, B., Hasenfuss, A., Villmann, T.: Batch and median neural gas. Neural Networks 19, 762–771 (2006)
Graepel, T., Obermayer, K.: A stochastic self-organizing map for proximity data. Neural Computation 11, 139–155 (1999)
Haasdonk, B., Bahlmann, C.: Learning with Distance Substitution Kernels. In: Rasmussen, C.E., Bülthoff, H.H., Schölkopf, B., Giese, M.A. (eds.) DAGM 2004. LNCS, vol. 3175, pp. 220–227. Springer, Heidelberg (2004)
Hammer, B., Hasenfuss, A., Schleif, F.-M., Villmann, T.: Supervised median neural gas. In: Dagli, C., Buczak, A., Enke, D., Embrechts, A., Ersoy, O. (eds.) Intelligent Engineering Systems Through Artificial Neural Networks 16, Smart Engineering System Design, pp. 623–633. ASME Press, New York (2006)
Hammer, B., Hasenfuss, A., Schleif, F.-M., Villmann, T.: Supervised batch neural gas. In: Schwenker, F., Marinai, S. (eds.) ANNPR 2006. LNCS (LNAI), vol. 4087, pp. 33–45. Springer, Heidelberg (2006)
Hammer, B., Micheli, A., Sperduti, A., Strickert, M.: Recursive self-organizing network models. Neural Networks 17(8-9), 1061–1086 (2004)
Heskes, T.: Energy functions for self-organizing maps. In: Oja, E., Kaski, S. (eds.) Kohonen maps, pp. 303–315. Elsevier, Amsterdam (1999)
MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: LeCam, L.M., Neyman, J. (eds.) Proc. 5th Berkeley Symposium on Math. Stat. and Prob., pp. 281–297. University of California Press, Berkeley (1967)
Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995)
Kohonen, T., Somervuo, P.: How to make large self-organizing maps for nonvectorial data. Neural Networks 15, 945–952 (2002)
Martinetz, T., Berkovich, S.G., Schulten, K.J.: Neural-gas network for vector quantization and its application to time-series prediction. IEEE Transactions on Neural Networks 4, 558–569 (1993)
Martinetz, T., Schulten, K.J.: Topology representing networks. Neural Networks 7(3), 507–522 (1994)
Mevissen, H., Vingron, M.: Quantifying the local reliability of a sequence alignment. Protein Engineering 9, 127–132 (1996)
Neuhaus, M., Bunke, H.: Edit distance based kernel functions for structural pattern classification. Pattern Recognition 39(10), 1852–1863 (2006)
Qin, A.K., Suganthan, P.N.: Kernel neural gas algorithms with application to cluster analysis. In: ICPR 2004, vol. 4, pp. 617–620 (2004)
Seo, S., Obermayer, K.: Self-organizing maps and clustering methods for matrix data. Neural Networks 17, 1211–1230 (2004)
Yin, H.: On the equivalence between kernel self-organising maps and self-organising mixture density network. Neural Networks 19(6), 780–784 (2006)
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Hasenfuss, A., Hammer, B., Schleif, FM., Villmann, T. (2007). Neural Gas Clustering for Dissimilarity Data with Continuous Prototypes. In: Sandoval, F., Prieto, A., Cabestany, J., Graña, M. (eds) Computational and Ambient Intelligence. IWANN 2007. Lecture Notes in Computer Science, vol 4507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73007-1_66
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DOI: https://doi.org/10.1007/978-3-540-73007-1_66
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