k-means++: few more steps yield constant approximation

Authors: Davin Choo, Christoph Grunau, Julian Portmann, Vaclav Rozhon

ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical In this paper, we improve their analysis to show that, for any arbitrarily small constant ε > 0, with only εk additional local search steps, one can achieve a constant approximation guarantee (with high probability in k), resolving an open problem in their paper. Our improvements rely on the following structural observation: After running k-means++, most of the clusters of the optimal solution are already well approximated with high probability in k.
Researcher Affiliation Academia 1ETH Z urich.
Pseudocode Yes Algorithm 1 k-means++ seeding; Algorithm 2 One step of Local Search++
Open Source Code No No explicit statement or link for open-source code is found in the paper.
Open Datasets No The paper is theoretical and does not use or evaluate on a specific public dataset.
Dataset Splits No The paper is theoretical and does not report on empirical experiments or data splits.
Hardware Specification No The paper is theoretical and does not describe hardware used for experiments.
Software Dependencies No The paper is theoretical and does not specify software dependencies with version numbers.
Experiment Setup No The paper is theoretical and does not provide details about an experimental setup or hyperparameters.