Abstract
In learning a geometric concept from examples, examples are mostly classified into two, positive examples and negative examples which are contained and not contained, respectively, in the concept. However, there exist cases where examples are classified into k classes. For example, clustering a concept space by the Voronoi diagram generated by k points is a very common tool used in image processing and many other areas. We call such a space a k-label space. The case of positive and negative examples corresponds to the 2-label space. In this paper, we first extend the ε-approximation for the 2-label space originally considered by Vapnik and Chervonenkis [10] (see also [1, 5]) to that for the k-label space. The generalized ε-approximation is then applied to the randomized algorithm for the assignment problem by Tokuyama and Nakano
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© 1993 Springer-Verlag Berlin Heidelberg
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Hasegawa, S., Imai, H., Ishiguro, M. (1993). ε-approximations of k-label spaces. In: Jantke, K.P., Kobayashi, S., Tomita, E., Yokomori, T. (eds) Algorithmic Learning Theory. ALT 1993. Lecture Notes in Computer Science, vol 744. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57370-4_55
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DOI: https://doi.org/10.1007/3-540-57370-4_55
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