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Metric k-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so a more sensible variant seeks for the best solution that disregards a given number z of points of the dataset, which are called outliers. We provide efficient algorithms for this important variant in the streaming model under the sliding window setting, where, at each time step, the dataset to be clustered is the window W of the most recent data items. For general metric spaces, our algorithms achieve O1 approximation and, remarkably, require a working memory linear in k+z and only logarithmic in |W|. For spaces of bounded doubling dimension, the approximation can be made arbitrarily close to 3. For these latter spaces, we show, as a by-product, how to estimate the effective diameter of the window W, which is a measure of the spread of the window points, disregarding a given fraction of noisy distances. We also provide experimental evidence of the practical viability of the improved clustering and diameter estimation algorithms.

In this paper we present novel streaming algorithms for the k-center and the diameter estimation problems for general metric spaces under the sliding window model. The key idea behind our algorithms is to maintain a small coreset which, at any time, allows to compute a solution to the problem under consideration for the current window, whose quality can be made arbitrarily close to the one of the best solution attainable by running a polynomial-time sequential algorithm on the entire window. Remarkably, the size of our coresets is independent of the window length and can be upper bounded by a function of the target number of centers (for the k-center problem), of the desired accuracy, and of the characteristics of the current window, namely its doubling dimension and aspect ratio. One of the major strengths of our algorithms is that they adapt obliviously to these two latter characteristics. We also provide experimental evidence of the practical viability of the algorithms and their superiority over the current state of the art.

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