Sliced Wasserstein Distance

Sliced Wasserstein distance (SWD) is a computationally efficient approximation of the Wasserstein distance, a metric for comparing probability distributions, addressing the latter's high computational cost in high dimensions. Current research focuses on improving SWD's accuracy and efficiency through various techniques, including optimizing projection directions (e.g., using energy-based distributions or Markov chains), developing novel SWD variants for specific data types (e.g., spherical data, point clouds, meshes), and integrating SWD into machine learning frameworks for tasks like generative modeling, shape correspondence, and domain adaptation. The resulting advancements enhance the applicability of optimal transport methods to a wider range of high-dimensional data and complex machine learning problems.