Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality
Efficiently and robustly analyzing shape data is critical across many scientific disciplines. While chirality is a fundamental property in numerous applications - most notably in molecular science - existing shape analysis metrics fail to distinguish between a shape and its mirror image. To address this gap, we introduce a multilinear generalization of the Gromov-Wasserstein objective. Under mild assumptions, this objective yields a distance between shapes, represented as probability distributions quotiented by a symmetry group $G$. In particular, for $G = SO(d)$, we introduce the Chiral Gromov-Wasserstein ($\mathrm{CGW}$) distance, sensitive to chirality. We establish robustness properti...
| Authors | Clément Soubrier, Geoffrey Woollard, Andrew Warren et al. |
|---|---|
| Primary category | math.OC |
| Published | 27 August 2026 |
| Last updated at source | 5 October 2026 |
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