Improved Smoothed Analysis of the k-Means Method

The k-means method is a widely used clustering algorithm. One of its distinguished features is its speed in practice. Its worst-case running-time, however, is exponential, leaving a gap between practical and theoretical performance. Arthur and Vassilvitskii [3] aimed at closing this gap, and they proved a bound of poly(nk , -1 ) on the smoothed runningtime of the k-means method, where n is the number of data points and is the standard deviation of the Gaussian perturbation. This bound, though better than the worstcase bound, is still much larger than the running-time observed in practice. We improve the smoothed analysis of the k-means method by showing two upper bounds on the expected running-time of k-means. First, we prove that the expected running-time is bounded by a polynomial in n k and -1 . Second, we prove an upper bound of kkd

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Bodo Manthey, Heiko Röglin
• Keywords: CORR 2008, Education, K-means, K-means Method, Upper Bound