International Journal of Computer Vision
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient and effective querying by image content
Journal of Intelligent Information Systems - Special issue: advances in visual information management systems
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Syntactic clustering of the Web
Selected papers from the sixth international conference on World Wide Web
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
High-dimensional computational geometry
High-dimensional computational geometry
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
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
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Clustering for metric and non-metric distance measures
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Clustering for metric and nonmetric distance measures
ACM Transactions on Algorithms (TALG)
Property testing
Property testing
Bregman clustering for separable instances
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Active clustering of biological sequences
The Journal of Machine Learning Research
| Hi-index | 0.00 |
We generalize the k-means algorithm presented by the authors [14] and show that the resulting algorithm can solve a larger class of clustering problems that satisfy certain properties (existence of a random sampling procedure and tightness). We prove these properties for the k-median and the discrete k-means clustering problems, resulting in O(2(k/ε)O(1)dn) time (1+ε)-approximation algorithms for these problems. These are the first algorithms for these problems linear in the size of the input (nd for n points in d dimensions), independent of dimensions in the exponent, assuming k and ε to be fixed. A key ingredient of the k-median result is a (1+ε)-approximation algorithm for the 1-median problem which has running time O(2(1/ε)O(1)d). The previous best known algorithm for this problem had linear running time.