Research map / Learning theory and algorithms / Clustering
Near-Optimal Algorithms for Explainable k-Medians and k-Means
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the previous greedy tree construction with randomized cuts that exclude cuts separating very close centers | Explainable k-medians ℓ1 · Explainable k-medians ℓ1 | competitive ratio: O(k) -> O(\log k\log\log k) | Helped |
| Embed squared Euclidean distances into ℓ1 with a coordinate-cut-preserving terminal embedding before constructing the tree | Explainable k-means · Explainable k-means | competitive ratio: O(k^2) -> O(k\log k \log\log k) | Helped |
| Use median-centered random threshold cuts and recursive splitting | Explainable k-medians ℓ2 · Explainable k-medians ℓ2 | competitive ratio: O(\log^{\nicefrac{3}{2}} k) | Helped |
| Require a threshold-tree solution for k-means | Explainable k-means · Explainable k-means | price of explainability: \Omega\rbr{\frac{k}{\log k}} | Hurt |
| Require a threshold-tree solution for ℓ2 k-medians | Explainable k-medians ℓ2 · Explainable k-medians ℓ2 | price of explainability: \Omega(\log k) | Hurt |
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