Optimal algorithms for approximate clustering
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Approximation schemes for Euclidean k-medians and related problems
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FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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Journal of the ACM (JACM)
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STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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A linear time algorithm for approximate 2-means clustering
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Preface: A brief overview of network algorithms
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SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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Computational Geometry: Theory and Applications
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Computational Geometry: Theory and Applications
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Computer Communications
Linear-time approximation schemes for clustering problems in any dimensions
Journal of the ACM (JACM)
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Pattern Recognition Letters
Bounded-hop energy-efficient broadcast in low-dimensional metrics via coresets
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Small space representations for metric min-sum k-clustering and their applications
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Minimum-energy broadcast with few senders
DCOSS'07 Proceedings of the 3rd IEEE international conference on Distributed computing in sensor systems
Clustering for metric and nonmetric distance measures
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Universal ε-approximators for integrals
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Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Property testing
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FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
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ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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ISMIS'05 Proceedings of the 15th international conference on Foundations of Intelligent Systems
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SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Some results on approximate 1-median selection in metric spaces
Theoretical Computer Science
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Journal of the ACM (JACM)
Clustering via geometric median shift over Riemannian manifolds
Information Sciences: an International Journal
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Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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ACM Computing Surveys (CSUR)
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Theoretical Computer Science
Twitter spammer detection using data stream clustering
Information Sciences: an International Journal
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In this paper, we show the existence of small coresets for the problems of computing k-median and k-means clustering for points in low dimension. In other words, we show that given a point set P in Rd, one can compute a weighted set S ⊆ P, of size O(k ε-d log n), such that one can compute the k-median/means clustering on S instead of on P, and get an (1+ε)-approximation. As a result, we improve the fastest known algorithms for (1+ε)-approximate k-means and k-median. Our algorithms have linear running time for a fixed k and ε. In addition, we can maintain the (1+ε)-approximate k-median or k-means clustering of a stream when points are being only inserted, using polylogarithmic space and update time.