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

Is Simple Uniform Sampling Effective for Center-Based Clustering with Outliers: When and Why?