Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
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
Coresets in dynamic geometric data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Smaller coresets for k-median and k-means clustering
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
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
Coresets forWeighted Facilities and Their Applications
FOCS '06 Proceedings of the 47th 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
Clustering for metric and non-metric distance measures
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for clustering uncertain data
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Facility Location in Dynamic Geometric Data Streams
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Coresets and approximate clustering for Bregman divergences
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Single facility collection depots location problem in the plane
Computational Geometry: Theory and Applications
Proceedings of the forty-first annual ACM symposium on Theory of computing
Clustering for metric and nonmetric distance measures
ACM Transactions on Algorithms (TALG)
Universal ε-approximators for integrals
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algorithms and theory of computation handbook
Improving the performance of k-means for color quantization
Image and Vision Computing
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
A near-linear algorithm for projective clustering integer points
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Data reduction for weighted and outlier-resistant clustering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Streaming k-means on well-clusterable data
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bregman clustering for separable instances
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
From high definition image to low space optimization
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
StreamKM++: A clustering algorithm for data streams
Journal of Experimental Algorithmics (JEA)
Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels
Information Sciences: an International Journal
Learning Big (Image) Data via Coresets for Dictionaries
Journal of Mathematical Imaging and Vision
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Given a point set P ⊆ Rd the k-means clustering problem is to find a set C=(c1,...,ck) of k points and a partition of P into k clusters C1,...,Ck such that the sum of squared errors ∑i=1k ∑p ∈ Ci |p -ci |22 is minimized. For given centers this cost function is minimized byassigning points to the nearest center.The k-means cost function is probably the most widely used cost function in the area of clustering.In this paper we show that every unweighted point set P has a weak (ε, k)-coreset of size Poly(k,1/ε) for the k-means clustering problem, i.e. its size is independent of the cardinality |P| of the point set and the dimension d of the Euclidean space Rd. A weak coreset is a weighted set S ⊆ P together with a set T such that T contains a (1+ε)-approximation for the optimal cluster centers from P and for every set of kcenters from T the cost of the centers for S is a (1±ε)-approximation of the cost for P.We apply our weak coreset to obtain a PTAS for the k-means clustering problem with running time O(nkd + d · Poly(k/ε) + 2Õ(k/ε)).