Noisy k-means++ Revisited
Abstract
The -means++ algorithm by Arthur and Vassilvitskii [SODA 2007] is a classical and time-tested algorithm for the -means problem. While being very practical, the algorithm also has good theoretical guarantees: its solution is -approximate, in expectation. In a recent work, Bhattacharya, Eube, Roglin, and Schmidt [ESA 2020] considered the following question: does the algorithm retain its guarantees if we allow for a slight adversarial noise in the sampling probability distributions used by the algorithm? This is motivated e.g. by the fact that computations with real numbers in -means++ implementations are inexact. Surprisingly, the analysis under this scenario gets substantially more difficult and the authors were able to prove only a weaker approximation guarantee of . In this paper, we close the gap by providing a tight, -approximate guarantee for the -means++ algorithm with noise.
Cite
@article{arxiv.2307.13685,
title = {Noisy k-means++ Revisited},
author = {Christoph Grunau and Ahmet Alper Özüdoğru and Václav Rozhoň},
journal= {arXiv preprint arXiv:2307.13685},
year = {2023}
}