Online $k$-means Clustering on Arbitrary Data Streams. (arXiv:2102.09101v4 [cs.LG] UPDATED)

We consider online $k$-means clustering where each new point is assigned to
the nearest cluster center, after which the algorithm may update its centers.
The loss incurred is the sum of squared distances from new points to their
assigned cluster centers. The goal over a data stream $X$ is to achieve loss
that is a constant factor of $L(X, OPT_k)$, the best possible loss using $k$
fixed points in hindsight.

We propose a data parameter, $\Lambda(X)$, such that for any …

arxiv clustering data data streams lg