Real-world datasets often contain outliers, and the presence of outliers can make the clustering problems to be much more challenging. In this paper, we propose a simple uniform sampling framework for solving three representative center-based clustering with outliers problems: $k$-center/median/means clustering with outliers. Our analysis is fundamentally different from the previous (uniform and non-uniform) sampling based ideas. To explain the effectiveness of uniform sampling in theory, we introduce a measure of "significance" and prove that the performance of our framework depends on the significance degree of the given instance. In particular, the sample size can be independent of the input data size $n$ and the dimensionality $d$, if we assume the given instance is "significant", which is in fact a fairly reasonable assumption in practice. Due to its simplicity, the uniform sampling approach also enjoys several significant advantages over the non-uniform sampling approaches in practice. To the best of our knowledge, this is the first work that systematically studies the effectiveness of uniform sampling from both theoretical and experimental aspects.

翻译：摘要：现实数据集常包含异常点，这些异常点的存在使聚类问题更具挑战性。本文提出一种简单均匀采样框架，用于解决三类典型的带异常点中心聚类问题：带异常点的$k$-中心/中位数/均值聚类。我们的分析与现有（均匀和非均匀）采样方法本质不同。为从理论上解释均匀采样的有效性，我们引入“显著性”度量，并证明框架性能取决于给定实例的显著性程度。特别地，若假设给定实例“显著”（这在实际中是一个相当合理的假设），则样本规模可与输入数据规模$n$和维度$d$无关。由于方法简单，均匀采样在实践中比非均匀采样更具备若干显著优势。据我们所知，这是首项从理论与实验两方面系统性研究均匀采样有效性的工作。