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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Adaptive Sampling for k-Means Clustering
verfasst von : Ankit Aggarwal, Amit Deshpande, Ravi Kannan
Erschienen in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Verlag: Springer Berlin Heidelberg
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We show that
adaptively
sampled
O
(
k
) centers give a constant factor bi-criteria approximation for the
k
-means problem, with a constant probability. Moreover, these
O
(
k
) centers contain a subset of
k
centers which give a constant factor approximation, and can be found using LP-based techniques of Jain and Vazirani [JV01] and Charikar et al. [CGTS02]. Both these algorithms run in effectively
O
(
nkd
) time and extend the
O
(log
k
)-approximation achieved by the
k
-means++ algorithm of Arthur and Vassilvitskii [AV07].