Local search methods for k-means with outliers

We study the problem of k -means clustering in the presence of outliers. The goal is to cluster a set of data points to minimize the variance of the points assigned to the same cluster, with the freedom of ignoring a small set of data points that can be labeled as outliers. Clustering with outliers has received a lot of attention in the data processing community, but practical, efficient, and provably good algorithms remain unknown for the most popular k -means objective. Our work proposes a simple local search-based algorithm for k -means clustering with outliers. We prove that this algorithm achieves constant-factor approximate solutions and can be combined with known sketching techniques to scale to large data sets. Using empirical evaluation on both synthetic and large-scale real-world data, we demonstrate that the algorithm dominates recently proposed heuristic approaches for the problem.