no code implementations • 16 Jul 2022 • Christoph Grunau, Ahmet Alper Özüdoğru, Václav Rozhoň, Jakub Tětek
In their seminal work, Arthur and Vassilvitskii [SODA 2007] asked about the guarantees for its following \emph{greedy} variant: in every step, we sample $\ell$ candidate centers instead of one and then pick the one that minimizes the new cost.
no code implementations • 2 Jul 2020 • Christoph Grunau, Václav Rozhoň
In this paper, we build on their ideas and show how to adapt several sequential and distributed $k$-means algorithms to the setting with outliers, but with substantially stronger theoretical guarantees: our algorithms output $(1+\varepsilon)z$ outliers while achieving an $O(1 / \varepsilon)$-approximation to the objective function.
no code implementations • ICML 2020 • Davin Choo, Christoph Grunau, Julian Portmann, Václav Rozhoň
The k-means++ algorithm of Arthur and Vassilvitskii (SODA 2007) is a state-of-the-art algorithm for solving the k-means clustering problem and is known to give an O(log k)-approximation in expectation.