EEMCS

Full text available as:

PDF - Univ. of Twente only 424 Kb

Official URL: http://dx.doi.org/10.1145/2027216.2027217

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 article, 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.

Export this item as:

• BibTeX
• XML

To request a copy of the PDF please email us request copy

To correct this item please ask your editor

Repository Staff Only: edit this item