Summary
Optimal (mass) transport (OT) is a mathematical theory that solves the problem of how to find the best assignment between two general objects, e.g. two lists of points, in the most cost efficient way. It was originally formulated by Monge in 1791 in the context of matching supply to demand and further developed by Kantorovich in the 20th century who enabled its application in a more general setting and inspired the development of the Wasserstein distance. This distance provides a mathematical tool to measure distances between functions, histograms or more general objects. Compared to most commonly used distances one of its main benefits is that it takes into account the geometry of the underlying space. This presentation gives a short introduction into OT and the Wasserstein distance.
Files
The slides of the presentation are here.