Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Learning in Neural Networks: Theoretical Foundations
Learning in Neural Networks: Theoretical Foundations
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Empirical Risk Approximation: An Induction Principle for Unsupervised Learning
Empirical Risk Approximation: An Induction Principle for Unsupervised Learning
Optimal Time Bounds for Approximate Clustering
Machine Learning
A k-Median Algorithm with Running Time Independent of Data Size
Machine Learning
The minimax distortion redundancy in empirical quantizer design
IEEE Transactions on Information Theory
Combining partitions by probabilistic label aggregation
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
A discriminative framework for clustering via similarity functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximate clustering without the approximation
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Clustering Stability: An Overview
Foundations and Trends® in Machine Learning
Approximation algorithms for tensor clustering
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Active clustering of biological sequences
The Journal of Machine Learning Research
Stratified k-means clustering over a deep web data source
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
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We consider a framework of sample-based clustering. In this setting, the input to a clustering algorithm is a sample generated i.i.d by some unknown arbitrary distribution. Based on such a sample, the algorithm has to output a clustering of the full domain set, that is evaluated with respect to the underlying distribution. We provide general conditions on clustering problems that imply the existence of sampling based clustering algorithms that approximate the optimal clustering. We show that the K-median clustering, as well as K-means and the Vector Quantization problems, satisfy these conditions. Our results apply to the combinatorial optimization setting where, assuming that sampling uniformly over an input set can be done in constant time, we get a sampling-based algorithm for the K-median and K-means clustering problems that finds an almost optimal set of centers in time depending only on the confidence and accuracy parameters of the approximation, but independent of the input size. Furthermore, in the Euclidean input case, the dependence of the running time of our algorithm on the Euclidean dimension is only linear. Our main technical tool is a uniform convergence result for center based clustering that can be viewed as showing that the effective VC-dimension of k-center clustering equals k.