# Scalable k-Means Clustering via Lightweight Coresets

## TL;DR

This paper introduces lightweight coresets for k-means clustering that allow for both multiplicative and additive errors, enabling faster, smaller, and more versatile data summaries for large-scale clustering tasks.

## Contribution

The paper presents a novel algorithm for constructing lightweight coresets that handle both error types, generalizes to statistical clustering, and improves efficiency and summary size.

## Key findings

- Faster coreset construction algorithm than existing methods
- Coresets are smaller and more versatile for various clustering models
- Outperforms existing data summarization strategies in experiments

## Abstract

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.