Sliced Inner Product Gromov-Wasserstein Distances
The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing techniques offer an appealing route to scalability, but, unlike Wasserstein distances, GW problems do not generally admit closed-form solutions in one-dimension. We resolve this problem for the GW problem with inner product cost (IGW), propose a sliced IGW distance that enjoys a natural rotational invariance property, and comprehensively study its structural and computational properties. Numerical experiments validating our theory are presented, followed by ap...
| Authors | Xiaoyun Gong, Gabriel Rioux, Ziv Goldfeld |
|---|---|
| Primary category | stat.ML |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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