Bi-criteria sublinear time algorithms for clustering with outliers in high dimensions

Abstract

Real-world datasets often contain outliers, and the presence of outliers can make clustering problems be much more challenging. Existing algorithms for clustering with outliers often have high computational complexities. In this paper, we propose a simple yet effective sublinear framework for solving the representative center-based clustering with outliers problems: $k$-median/means clustering with outliers. Our analysis is fundamentally different from the previous (uniform and non-uniform) sampling based ideas. In particular, our sample complexity is independent of the input size and dimensionality, and thus it is suitable for dealing with large-scale and high-dimensional datasets. We also conduct a set of experiments to evaluate the effectiveness of our proposed method on both synthetic and real datasets.