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arXiv · 2211.15118

A Faster $k$-means++ Algorithm

Jiehao Liang·Somdeb Sarkhel·Zhao Song·Chenbo Yin·Junze Yin·Danyang Zhuo
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Abstract

$k$-means++ is an important algorithm for choosing initial cluster centers for the $k$-means clustering algorithm. In this work, we present a new algorithm that can solve the $k$-means++ problem with nearly optimal running time. Given $n$ data points in $\mathbb{R}^d$, the current state-of-the-art algorithm runs in $\widetilde{O}(k )$ iterations, and each iteration takes $\widetilde{O}(nd k)$ time. The overall running time is thus $\widetilde{O}(n d k^2)$. We propose a new algorithm \textsc{FastKmeans++} that only takes in $\widetilde{O}(nd + nk^2)$ time, in total.

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Jiehao Liang, Somdeb Sarkhel, Zhao Song, Chenbo Yin, Junze Yin, Danyang Zhuo. 2022-11-28. A Faster $k$-means++ Algorithm. https://arxiv.org/abs/2211.15118

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