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Distributional clustering of words for text classification
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Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
A Nearly Linear-Time Approximation Scheme for the Euclidean kappa-median Problem
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A divisive information theoretic feature clustering algorithm for text classification
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Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
Distributional clustering of English words
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On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Optimal Time Bounds for Approximate Clustering
Machine Learning
A Simple Linear Time (1+ ") -Approximation Algorithm for k-Means Clustering in Any Dimensions
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quick k-Median, k-Center, and Facility Location for Sparse Graphs
SIAM Journal on Computing
On k-Median clustering in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
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Clustering with Bregman Divergences
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A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Linear time algorithms for clustering problems in any dimensions
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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IEEE Transactions on Neural Networks
Mixed Bregman Clustering with Approximation Guarantees
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
Coresets and approximate clustering for Bregman divergences
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Worst-Case and Smoothed Analysis of k-Means Clustering with Bregman Divergences
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximation algorithms for tensor clustering
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Clustering for metric and nonmetric distance measures
ACM Transactions on Algorithms (TALG)
Cluster editing problem for points on the real line: A polynomial time algorithm
Information Processing Letters
Proximity algorithms for nearly-doubling spaces
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Channel capacity restoration of noisy optical quantum channels
NEHIPISIC'11 Proceeding of 10th WSEAS international conference on electronics, hardware, wireless and optical communications, and 10th WSEAS international conference on signal processing, robotics and automation, and 3rd WSEAS international conference on nanotechnology, and 2nd WSEAS international conference on Plasma-fusion-nuclear physics
On nonmetric similarity search problems in complex domains
ACM Computing Surveys (CSUR)
Bregman clustering for separable instances
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
TreeMatrix: A Hybrid Visualization of Compound Graphs
Computer Graphics Forum
Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels
Information Sciences: an International Journal
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Proceedings of the Third ACM SIGSPATIAL International Workshop on Querying and Mining Uncertain Spatio-Temporal Data
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We study a generalization of the k-median problem with respect to an arbitrary dissimilarity measure D. Given a finite set P, our goal is to find a set C of size k such that the sum of errors D(P, C) = Σp∈P minc∈C{D(p, c)} is minimized. The main result in this paper can be stated as follows: There exists an O(n2k/ε)O(1)) time (1 + ε)-approximation algorithm for the k-median problem with respect to D, if the 1-median problem can be approximated within a factor of (1 + ε) by taking a random sample of constant size and solving the 1-median problem on the sample exactly. Using this characterization, we obtain the first linear time (1 + ε)-approximation algorithms for the k-median problem in an arbitrary metric space with bounded doubling dimension, for the Kullback-Leibler divergence (relative entropy), for Mahalanobis distances, and for some special cases of Bregman divergences. Moreover, we obtain previously known results for the Euclidean k-median problem and the Euclidean k-means problem in a simplified manner. Our results are based on a new analysis of an algorithm from [20].