Is Simple Uniform Sampling Effective for Center-Based Clustering with Outliers: When and Why?
This addresses clustering with outliers, a common challenge in data analysis, by providing a theoretically justified and practical method, though it is incremental as it builds on existing sampling ideas.
The paper tackles the problem of center-based clustering with outliers in real-world datasets by proposing a simple uniform sampling framework, showing that sample size can be independent of input data size and dimensionality under a 'significant' instance assumption.
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.