Scalable k-Means Clustering via Lightweight Coresets
This work addresses the challenge of efficient data summarization for clustering, offering a scalable solution that is embarrassingly parallel and applicable to various clustering types, though it is incremental as it builds on existing coreset concepts.
The authors tackled the problem of scaling clustering algorithms to massive datasets by introducing lightweight coresets that allow both multiplicative and additive approximation errors, resulting in faster construction, smaller coresets, and outperforming existing methods in experiments.
Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive data sets. While existing approaches generally only allow for multiplicative approximation errors, we propose a novel notion of lightweight coresets that allows for both multiplicative and additive errors. We provide a single algorithm to construct lightweight coresets for k-means clustering as well as soft and hard Bregman clustering. The algorithm is substantially faster than existing constructions, embarrassingly parallel, and the resulting coresets are smaller. We further show that the proposed approach naturally generalizes to statistical k-means clustering and that, compared to existing results, it can be used to compute smaller summaries for empirical risk minimization. In extensive experiments, we demonstrate that the proposed algorithm outperforms existing data summarization strategies in practice.