Bregman clustering for separable instances

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

Volumn 6139 LNCS, Issue , 2010, Pages 212-223

  Ackermann, Marcel R ^a   Blömer, Johannes ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE SOLUTION; ARITHMETIC OPERATIONS; BREGMAN DIVERGENCES; CONSTANT-FACTOR APPROXIMATION ALGORITHMS; EUCLIDEAN; FINITE SET; INPUT SET; K-MEANS; K-MEDIAN PROBLEM; TEXT CLASSIFICATION;

INFORMATION THEORY; SPEECH PROCESSING; TEXT PROCESSING;

APPROXIMATION ALGORITHMS;

EID: 77954651536     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-13731-0_21     Document Type: Conference Paper

References (29)

1. Arora, S., Raghavan, P., Rao, S.: Approximation schemes for Euclidean k-medians and related problems. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC '98), pp. 106-113 (1998)
2. Kolliopoulos, S.G., Rao, S.: A nearly linear-time approximation scheme for the Euclidean k-median problem. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 378-389. Springer, Heidelberg (1999)
3. Bǎdoiu, M., Har-Peled, S., Indyk, P.: Approximate clustering via core-sets. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC'02), pp. 250-257. Association for Computing Machinery (2002)
4. Har-Peled, S., Mazumdar, S.: On coresets for k-means and k-median clustering. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC'04), pp. 291-300. Association for Computing Machinery (2004)
5. Kumar, A., Sabharwal, Y., Sen, S.: Linear time algorithms for clustering problems in any dimensions. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1374-1385. Springer, Heidelberg (2005)
6. Chen, K.: On k-median clustering in high dimensions. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '06), pp. 1177- 1185. Society for Industrial and Applied Mathematics (2006)
7. Matoušek, J.: On approximate geometric k-clustering. Discrete and Computational Geometry 24(1), 61-84 (2000)
8. Fernandez de la Vega, W., Karpinski, M., Kenyon, C., Rabani, Y.: Approximation schemes for clustering problems. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing (STOC'03), pp. 50-58. Association for Computing Machinery (2003)
9. Kumar, A., Sabharwal, Y., Sen, S.: A simple linear time (1+ε)-approximation algorithm for k-means clustering in any dimensions. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS '04), pp. 454-462. IEEE Computer Society, Los Alamitos (2004)
10. Chen, K.: On coresets for k-median and k-means clustering in metric and Euclidean spaces and their applications. SIAM Journal on Computing 39(3), 923-947 (2009)
11. Feldman, D., Monemizadeh, M., Sohler, C.: A PTAS for k-means clustering based on weak coresets. In: Proceedings of the 23rd ACM Symposium on Computational Geometry (SCG '07), pp. 11-18. Association for Computing Machinery (2007)
12. Ackermann, M.R., Blömer, J., Sohler, C.: Clustering for metric and non-metric distance measures. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '08), pp. 799-808. Society for Industrial and Applied Mathematics (2008); Full version to appear in ACM Transactions on Algorithms (special issue on SODA '08).
13. Ackermann, M.R., Blömer, J.: Coresets and approximate clustering for Bregman divergences. In: Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'09), pp. 1088-1097. Society for Industrial and Applied Mathematics (2009)
14. Lloyd, S.P.: Least squares quantization in PCM. IEEE Transactions on Information Theory 28(2), 129-137 (1982)
15. Arthur, D., Manthey, B., Röglin, H.: k-means has polynomial smoothed complexity. In: Proceedings of the 50th Symposium on Foundations of Computer Science (FOCS '09). IEEE Computer Society Press, Los Alamitos (2009) (to appear)
16. Vattani, A.: k-means requires exponetially many iterations even in the plane. In: Proceedings of the 25th Annual Symposium on Computational Geometry (SCG '09), pp. 324-332. Association for Computing Machinery (2009)
17. Arthur, D., Vassilvitskii, S.: k-means++: the advantages of careful seeding. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '07), pp. 1027-1035. Society for Industrial and Applied Mathematics (2007)
18. Ostrovsky, R., Rabani, Y., Schulman, L.J., Swamy, C.: The effectiveness of Lloydtype methods for the k-means problem. In: Proceedings of the 47th Annual Symposium on Foundations of Computer Science (FOCS '06), pp. 165-176. IEEE Computer Society, Los Alamitos (2006)
19. Aggarwal, A., Deshpande, A., Kannan, R.: Adaptive sampling for k-means clustering. In: Proceedings of the 12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX '09), pp. 15-28. Springer, Heidelberg (2009)
20. Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with Bregman divergences. Journal of Machine Learning Research 6, 1705-1749 (2005)
21. Banerjee, A., Guo, X., Wang, H.: On the optimality of conditional expectation as a Bregman predictor. IEEE Transactions on Information Theory 51(7), 2664-2669 (2005) (Pubitemid 41136414)
22. Manthey, B., Röglin, H.: Worst-case and smoothed analysis of k-means clustering with Bregman divergences. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 1024-1033. Springer, Heidelberg (2009)
23. Nock, R., Luosto, P., Kivinen, J.: Mixed Bregman clustering with approximation guarantees. In: Daelemans, W., Goethals, B., Morik, K. (eds.) ECML PKDD 2008, Part II. LNCS (LNAI), vol. 5212, pp. 154-169. Springer, Heidelberg (2008)
24. Sra, S., Jegelka, S., Banerjee, A.: Approximation algorithms for Bregman clustering, co-clustering and tensor clustering. Technical Report MPIK-TR-177, Max Planck Institure for Biological Cybernetics (2008)
25. Kanungo, T., Mount, D.M., Netanyahu, N.S., Piatko, C.D., Silverman, R., Wu, A.Y.: An efficient k-means clustering algorithm: Analysis and implementation. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(7), 881-892 (2002)
26. Ben-Hur, A., Elisseeff, A., Guyon, I.: A stability based method for discovering structure in clustered data. In: Proceedings of the 7th Pacific Symposium on Biocomputing (PSB '02), pp. 6-17. World Scientific, Singapore (2002)
27. Bregman, L.M.: The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics 7, 200-217 (1967)
28. Mahalanobis, P.C.: On the generalized distance in statistics. In: Proceedings of the National Institute of Sciences of India, vol. 2(1), pp. 49-55. Indian National Science Academy (1936)
29. Ackermann, M.R.: Algorithms for the Bregman k-Median Problem. PhD thesis, University of Paderborn, Department of Computer Science (2009)