In this paper, we show that for several clustering problems one can extract a small set of points, so that using those core-sets enable us to perform approximate clustering efficiently.Expand

We present a general ϵ-approximation algorithm for approximating various descriptors of the extent of a set <i>P</i> of points in R<sup><i>d</i></sup> with the property that (1 − ϵ)μ(<i> P</i>) ≤ μ(< i>Q</i>.Expand

We study generalization properties of the area under the ROC curve (AUC), a quantity that has been advocated as an evaluation criterion for the bipartite ranking problem.Expand

In this paper, we show the existence of small coresets for the problems of computing k-median and k-means clustering for points in low dimension.Expand

The paradigm of coresets has recently emerged as a powerful tool for efficiently approximating various extent measures of a point set P . Using this paradigm, one quickly computes a small subset Q of… Expand

The average number of visits to a > 0 before returning to the origin is 1 (hint: show that it is closely related to the expectation of some geometric random variable).Expand

We study the problem of finding a disk covering the largest number of red points, while avoiding all the blue points, and provide a near-linear expected-time randomized approximation algorithm for this problem.Expand