期刊
JOURNAL OF THE ACM
卷 58, 期 5, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/2027216.2027217
关键词
Algorithms; Theory; Data clustering; k-means method; smoothed analysis
类别
资金
- German Academic Exchange Service (DAAD)
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.
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