Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
On k-Median clustering in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The Effectiveness of Lloyd-Type Methods for the k-Means Problem
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Clustering with Bregman Divergences
The Journal of Machine Learning Research
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
k-means++: the advantages of careful seeding
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Clustering for metric and non-metric distance measures
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
k-means requires exponentially many iterations even in the plane
Proceedings of the twenty-fifth annual symposium on Computational geometry
Adaptive Sampling for k-Means Clustering
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Worst-Case and Smoothed Analysis of k-Means Clustering with Bregman Divergences
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
k-Means Has Polynomial Smoothed Complexity
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Linear time algorithms for clustering problems in any dimensions
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the optimality of conditional expectation as a Bregman predictor
IEEE Transactions on Information Theory
Approximate bregman near neighbors in sublinear time: beyond the triangle inequality
Proceedings of the twenty-eighth annual symposium on Computational geometry
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The Bregman k-median problem is defined as follows. Given a Bregman divergence Dφ and a finite set $P \subseteq {\mathbb R}^d$ of size n, our goal is to find a set C of size k such that the sum of errors cost(P,C)=∑p∈P min c∈C Dφ(p,c) is minimized. The Bregman k-median problem plays an important role in many applications, e.g., information theory, statistics, text classification, and speech processing. We study a generalization of the kmeans++ seeding of Arthur and Vassilvitskii (SODA '07). We prove for an almost arbitrary Bregman divergence that if the input set consists of k well separated clusters, then with probability $2^{-{\mathcal O}(k)}$ this seeding step alone finds an ${\mathcal O}(1)$-approximate solution. Thereby, we generalize an earlier result of Ostrovsky et al. (FOCS '06) from the case of the Euclidean k-means problem to the Bregman k-median problem. Additionally, this result leads to a constant factor approximation algorithm for the Bregman k-median problem using at most $2^{{\mathcal O}(k)}n$ arithmetic operations, including evaluations of Bregman divergence Dφ.