| F. Leisch, A. Weingessel, and E. Dimitriadou, \Competitive learning for binary valued data," in Proceedings of the 8th International Conference on Articial Neural Networks (ICANN 98) (L. Niklasson, M. Boden, and T. Ziemke, eds.), vol. 2, (Skovde, Sweden), pp. 779-784, Springer, Sept. 1998. |
....such that the center of each cluster is simply the mean of the cluster and Equation 1 is the sum of the within cluster variances. If absolute distance is used, then the correct cluster centers are the respective medians. Recently several extensions to non Euclidean distances have been proposed [5], 6] Popular partitioning algorithms include classic methods like the k means algorithm and its online variants (which are often called hard competitive learning) More recent algorithms like the neural gas algorithm [7] or SOMs [8] also fall into this category, but add some regularization ....
F. Leisch, A. Weingessel, and E. Dimitriadou, \Competitive learning for binary valued data," in Proceedings of the 8th International Conference on Articial Neural Networks (ICANN 98) (L. Niklasson, M. Boden, and T. Ziemke, eds.), vol. 2, (Skovde, Sweden), pp. 779-784, Springer, Sept. 1998.
....in Steiner (1998) A more formal treatment of the xpoint method applied to a general class of optimization problems can be found in P otzelberger Strasser (1997) 2. 2 Hard Competitive Learning with Binary Distance Measure Another modi cation of a standard cluster algorithm is proposed by Leisch et al. 1998). They take hard competitive learning as base algorithm and replace the usual symmetric distances such as Euclidean or absolute distance by asymmetric binary distances. Binary distances can be useful, if a common 1 between two binary vectors is more important than a common 0 . Consider two ....
....1990) D(x; y) as distance D between x and y. Since D does not depend on , dimensions where both vectors are 0 are ignored. This distance counts the number of di erent components in x and y and divides it by the number of components, where at least one 1 appears. See Leisch et al. 1998) for technical details. Note that the combination of hard competitive learning with binary distances is still work in progress and that the proposed algorithm is not fully mature yet. 2 st 1 st 2 st 3 st 4 total average dependent 1a 6.0 6.0 6.0 6.0 6.0 dependent 2 6.0 6.0 6.0 6.0 6.0 dependent ....
Leisch, F., Weingessel, A., & Dimitriadou, E. (1998). Competitive learning for binary valued data. In Niklasson, L., Boden, M., & Ziemke, T. (eds.), Proceedings of the 8th International Conference on Articial Neural Networks (ICANN 98), vol. 2, pp. 779-784, Skovde, Sweden.
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