NP-hardness of Euclidean sum-of-squares clustering
- 4.5k Downloads
A recent proof of NP-hardness of Euclidean sum-of-squares clustering, due to Drineas et al. (Mach. Learn. 56:9–33, 2004), is not valid. An alternate short proof is provided.
KeywordsClustering Sum-of-squares Complexity
- Aloise, D., & Hansen, P. (2007). On the complexity of minimum sum-of-squares clustering. Cahiers du GERAD, G-2007-50, July 2007, available online at http://www.gerad.ca.
- Arthur, D., & Vassilvitskii, S. (2007). K-means++: the advantages of careful seeding. In 2007 ACM-SIAM symposium on discrete algorithms (SODA’07). Google Scholar
- Dasgupta, S. (2008). The hardness of k -means clustering (Technical Report CS2008-0916). University of California, 17 January 2008. Google Scholar
- Deshpande, A., & Popat, P. (2008). Email sent to Ravi Kannan et al. and transmitted by Nina Mishra to the first and third authors. 22 January 2008. Google Scholar
- Kanade, G., Nimbhorkar, P., & Varadarajan, K. (2008). On the NP-hardness of the 2-means problem. Manuscript of 14 February 2008. Google Scholar
- MacQueen, J. B. (1967). Some methods for classification and analysis of multivariate observations. In Proceedings of 5th Berkeley symposium on mathematical statistics and probability (Vol. 2, pp. 281–297), Berkeley, CA. Google Scholar
- Ostrovsky, R., Rabani, Y., Schulman, L. J., & Swamy, C. (2006). The effectiveness of Lloyd-type methods for the k-means problem. In Proceedings of the 47th annual IEEE symposium on foundations of computer science (FOCS’06). Google Scholar
© Springer Science+Business Media, LLC 2009