node2coords: Graph Representation Learning with Wasserstein Barycenters

TL;DR

node2coords introduces an interpretable graph representation learning method using Wasserstein barycenters, capturing key structural information and robustness to graph perturbations, with competitive results in node classification.

Contribution

It proposes a novel autoencoder-based approach that learns low-dimensional graph representations with interpretability and robustness, utilizing Wasserstein barycenters for the first time in this context.

Findings

Learned representations are interpretable and reveal structural patterns.

Embeddings are stable under graph perturbations.

Achieves competitive or superior node classification performance.

Abstract

In order to perform network analysis tasks, representations that capture the most relevant information in the graph structure are needed. However, existing methods do not learn representations that can be interpreted in a straightforward way and that are robust to perturbations to the graph structure. In this work, we address these two limitations by proposing node2coords, a representation learning algorithm for graphs, which learns simultaneously a low-dimensional space and coordinates for the nodes in that space. The patterns that span the low dimensional space reveal the graph's most important structural information. The coordinates of the nodes reveal the proximity of their local structure to the graph structural patterns. In order to measure this proximity by taking into account the underlying graph, we propose to use Wasserstein distances. We introduce an autoencoder that employs a linear layer in the encoder and a novel Wasserstein barycentric layer at the decoder. Node connectivity descriptors, that capture the local structure of the nodes, are passed through the encoder to learn the small set of graph structural patterns. In the decoder, the node connectivity descriptors are reconstructed as Wasserstein barycenters of the graph structural patterns. The optimal weights for the barycenter representation of a node's connectivity descriptor correspond to the coordinates of that node in the low-dimensional space. Experimental results demonstrate that the representations learned with node2coords are interpretable, lead to node embeddings that are stable to perturbations of the graph structure and achieve competitive or superior results compared to state-of-the-art methods in node classification.