Abstract
The well-known ’k-means’ clustering can be regarded as an approximation of a given distribution (which can be a sample) by a set of optimally chosen k points. However, in many cases approximative sets of different types are of interest. For example, approximation of a distribution by circles is important in allocating communication stations, the circles being interpreted as working areas of the stations. The paper covers two related topics. First we propose a heuristic algorithm to find k circles of a given radius r that fit with the planar data set. Then we analyse the problem of consistency: does a sequence of sample-based sets of optimal circles converge to the class of optimal circles for the population? The positive answer is given for arbitrary finite-dimensional normed linear spaces.
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© 1999 Springer-Verlag Berlin · Heidelberg
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Pärna, K., Lember, J., Viiart, A. (1999). Approximation of Distributions by Sets. In: Gaul, W., Locarek-Junge, H. (eds) Classification in the Information Age. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60187-3_21
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DOI: https://doi.org/10.1007/978-3-642-60187-3_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65855-9
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