Transport Clustering: Solving Low-Rank Optimal Transport via Clustering
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport explicitly constrains the rank of the transport plan to infer latent structure. This improves statistical stability and robustness, yields sharper parametric rates for estimating Wasserstein distances adaptive to the intrinsic rank, and generalizes $K$-means to co-clustering. These advantages, however, come at the cost of a non-convex and NP-hard optimization problem. We introduce transport clustering, an algorithm to compute a low-rank OT plan that reduces...
| Authors | Henri Schmidt, Peter Halmos, Ben Raphael |
|---|---|
| Primary category | cs.LG |
| Published | 3 March 2026 |
| Last updated at source | 3 March 2026 |
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