Tree Metric

Tree metrics represent distances between points structured as a tree, enabling efficient computation of optimal transport (OT) and offering advantages over traditional methods like sliced Wasserstein distance, particularly in high-dimensional spaces. Current research focuses on developing robust algorithms for computing tree-based OT, even with noisy or incomplete tree structures, and applying these methods to diverse fields such as image processing, forestry monitoring, and music analysis. These advancements improve the accuracy and scalability of analyses involving hierarchical data, impacting fields requiring efficient computation of distances in complex, tree-like structures.