A Framework for Wasserstein-1-Type Metrics
This work provides a theoretical framework for researchers in optimal transport and machine learning, though it appears incremental as it builds on existing Wasserstein-1 metrics.
The authors proposed a unifying framework that generalizes the Wasserstein-1 metric to measure discrepancies between nonnegative measures of different mass, inheriting convexity and computational efficiency while encompassing previous approaches as special cases. They demonstrated the usefulness of specific instances through numerical experiments in applications.
We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the Wasserstein-1 metric, and it includes several previous approaches from the literature as special cases. For various specific instances of the generalized Wasserstein-1 metric we furthermore demonstrate their usefulness in applications by numerical experiments.