Differential Privacy for Clustering Under Continual Observation. (arXiv:2307.03430v1 [cs.DS])

We consider the problem of clustering privately a dataset in $\mathbb{R}^d$
that undergoes both insertion and deletion of points. Specifically, we give an
$\varepsilon$-differentially private clustering mechanism for the $k$-means
objective under continual observation. This is the first approximation
algorithm for that problem with an additive error that depends only
logarithmically in the number $T$ of updates. The multiplicative error is
almost the same as non privately. To do so we show how to perform dimension
reduction under continual observation …

algorithm clustering deletion differential privacy error privacy private problem under