Abstract
We define the k-center for a probability measure P on a separable metric space T as a system of k points of T providing the best approximation of P over all discrete k-point distributions (see loss function (1)). Searching for a class of spaces where each P has at least one k-center we reached the class of reflexive separable Banach spaces. In these spaces the weak convergence of k-centers corresponding to a weakly converging sequence of measures has been shown.
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© 1992 Springer-Verlag Berlin · Heidelberg
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Pärna, K. (1992). Clustering in Metric Spaces: Some Existence and Continuity Results for k-Centers. In: Schader, M. (eds) Analyzing and Modeling Data and Knowledge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46757-8_10
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DOI: https://doi.org/10.1007/978-3-642-46757-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54708-2
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