提出鲁棒k均值聚类，提升对异常值和分布偏移的抗性。
Distributionally Robust K-Means Clustering
- 基于Wasserstein-2球定义分布不确定性集，优化最坏情况下的聚类效果。
- 算法在标准数据集上显著提升异常值检测能力，噪声下聚类更稳定。
- 适合处理小样本、含异常数据的聚类任务，尤其适用于真实场景。
K-means聚类是无监督学习的核心方法，但对异常值、分布偏移和小样本极为敏感。将k-means视为经验分布的Lloyd-Max量化，本文提出一种分布鲁棒变体，通过假设真实分布位于经验分布的Wasserstein-2球内，构建最小最大优化目标，以最小化最坏情况下的期望平方距离。该方法导出可解的对偶形式，得到软聚类方案，用平滑权重替代硬分配。提出一种高效的块坐标下降算法，具有可证明的单调递减性和局部线性收敛性。在标准基准和大规模合成数据上的实验表明，该方法在异常值检测和抗噪能力方面均有显著提升。
原文摘要 · Abstract (English)
K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a distributionally robust variant that protects against such pathologies. We posit that the unknown population distribution lies within a Wasserstein-2 ball around the empirical distribution. In this setting, one seeks cluster centers that minimize the worst-case expected squared distance over this ambiguity set, leading to a minimax formulation. A tractable dual yields a soft-clustering scheme that replaces hard assignments with smoothly weighted ones. We propose an efficient block coordinate descent algorithm with provable monotonic decrease and local linear convergence. Experiments on standard benchmarks and large-scale synthetic data demonstrate substantial gains in outlier detection and robustness to noise.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。