Intrinsic Sliced Wasserstein Distances for Comparing Collections of Probability Distributions on Manifolds and Graphs

Understand

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics.

• In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs.
• This paper introduces an approach for detecting differences between two collections of distributions over such general domains.
• To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs.