Optimal Transport Distances for Directed, Weighted Graphs: A Case Study With Cell-Cell Communication Networks

IEEE International Conference on Acoustics Speech and Signal Processing

Abstract

Comparing graphs by means of optimal transport has recently gained significant attention, as the distances induced by optimal transport provide both a principled metric between graphs as well as an interpretable description of the associated changes between graphs in terms of a transport plan. As the lack of symmetry introduces challenges in the typically considered formulations, optimal transport distances for graphs have mostly been developed for undirected graphs. Here1, we propose two distance measures to compare directed graphs based on variants of optimal transport(OT): (i) an earth movers distance (Wasserstein) and (ii) a Gromov-Wasserstein (GW) distance. We evaluate these two distances and discuss their relative performance for both simulated graph data and real-world directed cell-cell communication graphs, inferred from single-cell RNA-seq data.

Authors 3

1. James Shiniti Nagai Aachen Institute for Computational Genomics

   RWTH Aachen University

   Affiliation as printed

   Institute for Computational Genomics,RWTH Aachen Medical Faculty,Germany

   RWTH Aachen Medical Faculty, Institute for Computational Genomics, Germany

2. Ivan G. Costa Aachen Institute for Computational Genomics

   RWTH Aachen University

   Affiliation as printed

   Institute for Computational Genomics,RWTH Aachen Medical Faculty,Germany

   RWTH Aachen Medical Faculty, Institute for Computational Genomics, Germany

3. Michael T. Schaub Aachen Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Department of Computer Science,Germany

   Department of Computer Science, RWTH Aachen University, Germany