eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-30
55:1
55:7
10.4230/LIPIcs.ESA.2023.55
article
Noisy k-Means++ Revisited
Grunau, Christoph
1
https://orcid.org/0000-0002-1057-9429
Özüdoğru, Ahmet Alper
1
Rozhoň, Václav
1
https://orcid.org/0000-0002-9646-8446
ETH Zürich, Switzerland
The k-means++ algorithm by Arthur and Vassilvitskii [SODA 2007] is a classical and time-tested algorithm for the k-means problem. While being very practical, the algorithm also has good theoretical guarantees: its solution is O(log k)-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 k-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 O(log² k). In this paper, we close the gap by providing a tight, O(log k)-approximate guarantee for the k-means++ algorithm with noise.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol274-esa2023/LIPIcs.ESA.2023.55/LIPIcs.ESA.2023.55.pdf
clustering
k-means
k-means++
adversarial noise