Embedding Directed Graphs in Potential Fields Using FastMap-D

TL;DR

FastMap-D is a novel algorithm that efficiently embeds directed graphs into Euclidean space by using potential fields and machine learning, enabling geometric analysis of asymmetric relationships.

Contribution

We introduce FastMap-D, a new method extending FastMap for directed graphs by incorporating potential fields learned via machine learning.

Findings

FastMap-D outperforms existing methods on various directed graph datasets.

The potential field approach effectively captures asymmetry in directed graphs.

FastMap-D enables geometric analysis of directed relationships.

Abstract

Embedding undirected graphs in a Euclidean space has many computational benefits. FastMap is an efficient embedding algorithm that facilitates a geometric interpretation of problems posed on undirected graphs. However, Euclidean distances are inherently symmetric and, thus, Euclidean embeddings cannot be used for directed graphs. In this paper, we present FastMap-D, an efficient generalization of FastMap to directed graphs. FastMap-D embeds vertices using a potential field to capture the asymmetry between the pairwise distances in directed graphs. FastMap-D learns a potential function to define the potential field using a machine learning module. In experiments on various kinds of directed graphs, we demonstrate the advantage of FastMap-D over other approaches.