Worst-case and smoothed analysis of k-means clustering with Bregman divergences

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

Volumn 5878 LNCS, Issue , 2009, Pages 1024-1033

  Manthey, Bodo ^a   Röglin, Heiko ^b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

BREGMAN DIVERGENCES; DATA POINTS; DATA SETS; EUCLIDEAN; GENERAL CLASS; K-MEANS; K-MEANS ALGORITHM; K-MEANS CLUSTERING; K-MEANS METHOD; LOWER BOUNDS; RELATIVE ENTROPY; SEMI-RANDOM; SIMILARITY MEASURE; SMOOTHED ANALYSIS; SQUARED EUCLIDEAN DISTANCE; STANDARD DEVIATION; THEORY AND PRACTICE; WEB PAGE;

CLUSTER ANALYSIS; COMPUTATION THEORY;

CLUSTERING ALGORITHMS;

EID: 75649121507     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-10631-6_103     Document Type: Conference Paper

References (15)

1. Ackermann, M.R., Blömer, J.: Coresets and approximate clustering for Bregman divergences. In: Proc. of the 20th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 1088-1097 (2009)
2. Ackermann, M.R., Blömer, J., Sohler, C.: Clustering for metric and non-metric distance measures. In: Proc. of the 19th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 799-808 (2008)
3. Arthur, D., Manthey, B., Röglin, H.: k-means has polynomial smoothed complexity. In: Proc. of the 50th Ann. IEEE Symp. on Found. of Computer Science, FOCS (to appear, 2009)
4. Arthur, D., Vassilvitskii, S.: Worst-case and smoothed analysis of the ICP algorithm, with an application to the k-means method. SIAM Journal on Computing 39(2), 766-782 (2009)
5. Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with Bregman divergences. Journal of Machine Learning Research 6, 1705-1749 (2005)
6. Berkhin, P.: Survey of clustering data mining techniques. Technical report, Accrue Software, San Jose, CA, USA (2002)
7. Dhillon, I.S., Mallela, S., Kumar, R.: A divisive information-theoretic feature clustering algorithm for text classification. Journal of Machine Learning Research 3, 1265-1287 (2003)
8. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley & Sons, Chichester (2000)
9. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. II. John Wiley & Sons, Chichester (1971)
10. Gray, R.M., Buzo, A., Gray Jr., A.H., Matsuyama, Y.: Distortion measures for speech processing. IEEE Transactions on Acoustics, Speech, and Signal Processing 28(4), 367-376 (1980)
11. Inaba, M., Katoh, N., Imai, H.: Variance-based k-clustering algorithms by Voronoi diagrams and randomization. IEICE Transactions on Information and Systems E83-D(6), 1199-1206 (2000)
12. Lloyd, S.P.: Least squares quantization in PCM. IEEE Transactions on Information Theory 28(2), 129-137 (1982)
13. Manthey, B., Röglin, H.: Improved smoothed analysis of the k-means method. In: Proc. of the 20th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 461-470 (2009)
14. Spielman, D.A., Teng, S.-H.: Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time. Journal of the ACM 51(3), 385-463 (2004)
15. Vattani, A.: k-means requires exponentially many iterations even in the plane. In: Proc. of the 25th ACM Symp. on Computational Geometry (SoCG), pp. 324-332 (2009)