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• W3181595977 abstract "We consider the problem of explainable $k$-medians and $k$-means introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian~(ICML 2020). In this problem, our goal is to find a threshold decision tree that partitions data into $k$ clusters and minimizes the $k$-medians or $k$-means objective. The obtained clustering is easy to interpret because every decision node of a threshold tree splits data based on a single feature into two groups. We propose a new algorithm for this problem which is $tilde O(log k)$ competitive with $k$-medians with $ell_1$ norm and $tilde O(k)$ competitive with $k$-means. This is an improvement over the previous guarantees of $O(k)$ and $O(k^2)$ by Dasgupta et al (2020). We also provide a new algorithm which is $O(log^{3/2} k)$ competitive for $k$-medians with $ell_2$ norm. Our first algorithm is near-optimal: Dasgupta et al (2020) showed a lower bound of $Omega(log k)$ for $k$-medians; in this work, we prove a lower bound of $tildeOmega(k)$ for $k$-means. We also provide a lower bound of $Omega(log k)$ for $k$-medians with $ell_2$ norm." @default.
• W3181595977 created "2021-07-19" @default.
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• W3181595977 date "2021-07-02" @default.
• W3181595977 modified "2023-09-27" @default.
• W3181595977 title "Near-optimal Algorithms for Explainable k-Medians and k-Means" @default.
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