Convergence of online $k$-means
Machine Learning
2022-02-23 v1
Abstract
We prove asymptotic convergence for a general class of -means algorithms performed over streaming data from a distribution: the centers asymptotically converge to the set of stationary points of the -means cost function. To do so, we show that online -means over a distribution can be interpreted as stochastic gradient descent with a stochastic learning rate schedule. Then, we prove convergence by extending techniques used in optimization literature to handle settings where center-specific learning rates may depend on the past trajectory of the centers.
Keywords
Cite
@article{arxiv.2202.10640,
title = {Convergence of online $k$-means},
author = {Sanjoy Dasgupta and Gaurav Mahajan and Geelon So},
journal= {arXiv preprint arXiv:2202.10640},
year = {2022}
}