1 research outputs found
Is Simple Uniform Sampling Efficient for Center-Based Clustering With Outliers: When and Why?
Clustering has many important applications in computer science, but
real-world datasets often contain outliers. The presence of outliers can make
the clustering problems to be much more challenging. In this paper, we propose
a framework for solving three representative center-based clustering with
outliers problems: -center/median/means clustering with outliers. The
framework actually is very simple, where we just need to take a small uniform
sample from the input and run an existing approximation algorithm on the
sample. However, 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 "significance" criterion 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 and the dimensionality , if we assume the given instance is
sufficiently "significant", which is in fact a fairly appropriate assumption in
practice. Due to its simplicity, the uniform sampling approach also enjoys
several significant advantages over the non-uniform sampling approaches. The
experiments suggest that our framework can achieve comparable clustering
results with existing methods, but is much easier to implement and can greatly
reduce the running times. 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.Comment: arXiv admin note: text overlap with arXiv:1905.1014