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16979 k-Means has polynomial smoothed complexity
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Arthur, D. and Manthey, B. and Röglin, H. (2009) k-Means has polynomial smoothed complexity. In: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009), 24-27 Oct 2009, Atlanta, GA, USA. pp. 405-414. IEEE Computer Society. ISBN 978-0-7695-3850-1

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Official URL: http://doi.ieeecomputersociety.org/10.1109/FOCS.2009.14

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Abstract

The k-means method is one of the most widely used clustering algorithms, drawing its popularity from its speed in practice. Recently, however, it was shown to have exponential worst-case running time. In order to close the gap between practical performance and theoretical analysis, the k-means method has been studied in the model of smoothed analysis. But even the smoothed analyses so far are unsatisfactory as the bounds are still super-polynomial in the number n of data points.

In this paper, we settle the smoothed running time of the k-means method. We show that the smoothed number of iterations is bounded by a polynomial in n and 1/sigma, where sigma is the standard deviation of the Gaussian perturbations. This means that if an arbitrary input data set is randomly perturbed, then the k-means method will run in expected polynomial time on that input set.

Item Type:Conference or Workshop Paper (Extended Abstract, Talk)
Research Group:EWI-DMMP: Discrete Mathematics and Mathematical Programming
Research Program:CTIT-IE&ICT: Industrial Engineering and ICT
Uncontrolled Keywords:Smoothed analyis, k-Means method, k-Means, Clustering, k-Means clustering, Probabilistic analysis
ID Code:16979
Status:Published
Deposited On:04 March 2010
Refereed:Yes
International:Yes
More Information:statisticsmetis

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