A simple D 2-sampling based PTAS for k-means and other clustering problems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7434 LNCS, Issue , 2012, Pages 13-24

  Jaiswal, Ragesh ^a   Kumar, Amit ^a   Sen, Sandeep ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTERING PROBLEMS; HIGH PROBABILITY; K POINTS; K-CENTER; K-MEANS; K-MEANS CLUSTERING; NONUNIFORM SAMPLING; OBJECTIVE FUNCTIONS; PROBABILITY PROPORTIONAL; SAMPLING-BASED;

APPROXIMATION ALGORITHMS;

COMBINATORIAL MATHEMATICS;

EID: 84865647079     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-32241-9_2     Document Type: Conference Paper

References (22)

1. Arthur, D., Vassilvitskii, S.: k-means++: the advantages of careful seeding. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 1027-1035 (2007)
2. Ailon, N., Jaiswal, R., Monteleoni, C.: Streaming k-means approximation. In: Advances in Neural Information Processing Systems, vol. 22, pp. 10-18 (2009)
3. Aggarwal, A., Deshpande, A., Kannan, R.: Adaptive Sampling for k-Means Clustering. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX 2009. LNCS, vol. 5687, pp. 15-28. Springer, Heidelberg (2009)
4. Broder, A., Glassman, S., Manasse, M., Zweig, G.: Syntactic clustering of the web
5. Faloutsos, C., Barber, R., Flickner, M., Hafner, J.: Efficient and effective querying by image content. Journal of Intelligent Information Systems (1994)
6. Deerwester, S., Dumais, S., Landauer, T., Furnas, G., Harshman, A.: Indexing by latent semantic analysis. Journal of the American Society for Information Science (1990)
7. Swain, M., Ballard, D.: Color indexing. International Journal of Computer Vision (1991)
8. Dasgupta, S.: The hardness of k-means clustering. Technical Report CS2008-0916, Department of Computer Science and Engineering. University of California San Diego (2008)
9. Lloyd, S.: Least squares quantization in PCM. IEEE Transactions on Information Theory 28(2), 129-137 (1982)
10. Arthur, D., Vassilvitskii, S.: How slow is the k-means method? In: Proc. 22nd Annual Symposium on Computational Geometry, pp. 144-153 (2006)
11. Ostrovsky, R., Rabani, Y., Schulman, L.J., Swamy, C.: The effectiveness of lloyd-type methods for the k-means problem. In: Proc. 47th IEEE FOCS, pp. 165-176 (2006)
12. Ackermann, M.R., Blömer, J.: Coresets and approximate clustering for bregman divergences. In: ACM SIAM Symposium on Discrete Algorithms, pp. 1088-1097 (2009)
13. Chen, K.: On k-median clustering in high dimensions. In: SODA, pp. 1177-1185 (2006)
14. Feldman, D., Monemizadeh, M., Sohler, C.: A ptas for k-means clustering based on weak coresets. In: Symposium on Computational Geometry, pp. 11-18 (2007)
15. Inaba, M., Katoh, N., Imai, H.: Applications of weighted voronoi diagrams and randomization to variance based k-clustering. In: Proceedings of the Tenth Annual Symposium on Computational Geometry, pp. 332-339 (1994)
16. Matousek, J.: On approximate geometric k-clustering. In: Discrete and Computational Geometry (2000)
17. Badoiu, M., Har-Peled, S., Indyk, P.: Approximate clustering via core-sets. In: STOC, pp. 250-257 (2002)
18. de la Vega, W.F., Karpinski, M., Kenyon, C., Rabani, Y.: Approximation schemes for clustering problems. In: ACM Symposium on Theory of Computing, pp. 50-58 (2003)
19. Har-Peled, S., Mazumdar, S.: On coresets for k-means and k-median clustering. In: ACM Symposium on Theory of Computing, pp. 291-300 (2004)
20. Kumar, A., Sabharwal, Y., Sen, S.: Linear-time approximation schemes for clustering problems in any dimensions. J. ACM 57(2) (2010)
21. Awasthi, P., Blum, A., Sheffet, O.: Stability yields a ptas for k-median and k-means clustering. In: FOCS, pp. 309-318 (2010)
22. Har-Peled, S., Sadri, B.: How fast is the k-means method? In: ACM SIAM Symposium on Discrete Algorithms, pp. 877-885 (2005)