Distributionally Robust K-Means Clustering
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 p...
| Authors | Vikrant Malik, Taylan Kargin, Babak Hassibi |
|---|---|
| Primary category | cs.LG |
| Published | 13 April 2026 |
| Last updated at source | 13 April 2026 |
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