| Autor: |
la Tour, Max Dupré, Henzinger, Monika, Saulpic, David |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 and combine it with a differentially private greedy approximation algorithm for $k$-means. We also partially extend our results to the $k$-median problem. |
| Databáze: |
arXiv |
| Externí odkaz: |
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