Original title: Optimal Transport with Cyclic Symmetry
Authors: Shoichiro Takeda, Yasunori Akagi, Naoki Marumo, Kenta Niwa
The article introduces speedy methods for optimal transport (OT) by tapping into a cyclic symmetry found in various real-world scenarios like image and urban planning. Their approach cleverly shrinks the OT problem by using this symmetry and smart optimization tricks, making it much more manageable. Instead of solving the full OT problem directly, their algorithms tackle a smaller, optimized version, achieving the best solution faster. They focus on two key OT setups: linear programming OT (LOT) and strongly convex-regularized OT, which includes a famous one called entropy-regularized OT (EROT). Tests reveal these methods’ effectiveness on data with strict or approximate cyclic symmetry. Essentially, this work pioneers the use of symmetry in OT research, making it a game-changer by speeding up solutions for various real-world problems through clever mathematical shortcuts.
Original article: https://arxiv.org/abs/2311.13147