This article briefly introduced Arthur and Vassilvitshii's work on \textbf{k-means++} algorithm and further generalized the center initialization process. It is found that choosing the most distant sample point from the nearest center as new center can mostly have the same effect as the center initialization process in the \textbf{k-means++} algorithm.
Cite
@article{arxiv.1903.10025,
title = {Generalization of k-means Related Algorithms},
author = {Yiwei Li},
journal= {arXiv preprint arXiv:1903.10025},
year = {2019}
}