Hybrid Merging Projection Wasserstein Distance for Semantics-Aware Optimal Transport

We introduce the Hybrid Merging Projection Wasserstein (HW) distance, a novel and efficient alternative to traditional projection-based optimal transport methods such as Sliced Wasserstein (SW). Unlike prior approaches that rely solely on random directions, HW combines data-driven projections, via the proposed Linear Merging Projection (LMP), with stochastic ones to enhance both expressiveness and robustness. LMP minimizes between-class variance, enabling smoother distribution alignment, while random projections ensure generalization. Across classification, distribution alignment, and color transfer tasks, HW consistently outperforms standard projection-based distances in both accuracy and efficiency.