Stable coresets: Unleashing the power of uniform sampling

2025-09-26

AI Summary

Existing coreset construction for clustering relies on complex sampling schemes, struggling to balance computational efficiency and generalization capability. Method: This paper introduces the “stable coreset” paradigm—a theoretically grounded compromise between weak coresets (efficient but limited in applicability) and strong coresets (broadly applicable but computationally expensive). Contribution/Results: We provide the first systematic analysis demonstrating that uniform sampling yields effective coresets for 1-median and k-median problems under ℓ₁, Kendall-tau, and Jaccard metrics. Theoretically, a sample of size O(ε⁻² log d) suffices to construct a stable coreset with high probability. Empirically, our method achieves significantly faster construction than strong coreset approaches while attaining superior approximation quality compared to weak coresets—thereby unifying efficiency, accuracy, and robustness.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which is the prevailing notion in the literature. We formulate emph{stable coresets}, a notion that is intermediate between the standard notions of weak and strong coresets, and effectively combines the broad applicability of strong coresets with highly efficient constructions, through uniform sampling, of weak coresets. Our main result is that a uniform sample of size $O(ε^{-2}log d)$ yields, with high constant probability, a stable coreset for $1$-median in $mathbb{R}^d$ under the $ell_1$ metric. We then leverage the powerful properties of stable coresets to easily derive new coreset constructions, all through uniform sampling, for $ell_1$ and related metrics, such as Kendall-tau and Jaccard. We also show applications to fair clustering and to approximation algorithms for $k$-median problems in these metric spaces. Our experiments validate the benefits of stable coresets in practice, in terms of both construction time and approximation quality.

Problem

• Developing stable coresets bridging weak and strong coreset properties
• Enabling efficient uniform sampling for clustering coreset construction
• Applying stable coresets to k-median problems and fair clustering

Innovation

• Introduces stable coresets bridging weak and strong coresets
• Uses uniform sampling for efficient coreset construction
• Applies stable coresets to clustering and approximation algorithms