Research map / Learning theory and algorithms / Clustering
k-means++: few more steps yield constant approximation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add εk LocalSearch++ steps after k-means++ | k-means++ · k-means objective | approximation ratio: O(log k) -> 10^{30} / ε^3 | Helped |
| Use εk local search steps instead of O(k log log k) steps | k-means++ + LocalSearch++ · k-means objective | number of local search steps for a constant approximation: O(k log log k) -> εk | Helped |
| Provide a high-probability guarantee rather than an expectation guarantee | k-means++ + LocalSearch++ · k-means objective | probability of constant approximation: 1 - exp(-Ω(k^{0.1})) | Helped |
Closest papers by meaning
- Multi-Swap k-Means++ (NeurIPS 2023 · similarity 0.91)
- A Constant-Factor Bi-Criteria Approximation Guarantee for k-means++ (NeurIPS 2016 · similarity 0.90)
- Improved Guarantees for k-means++ and k-means++ Parallel (NeurIPS 2020 · similarity 0.88)
- A Better k-means++ Algorithm via Local Search (ICML 2019 · similarity 0.87)
- Analyzing $D^\alpha$ seeding for $k$-means (ICML 2024 · similarity 0.84)
- Near-Linear Time Approximation Algorithms for k-means with Outliers (ICML 2024 · similarity 0.84)
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