A Statistical Relational Approach to Learning Distance-based GCNs

TL;DR

This paper introduces a novel method for learning distance-based GCNs by embedding relational data into Euclidean space, constructing a secondary graph based on distances, and demonstrating its advantages through extensive empirical evaluation.

Contribution

The paper proposes a new approach that emphasizes learning a secondary Euclidean graph using relational density estimation, outperforming existing GCN and relational embedding methods.

Findings

Outperforms 12 GCN and relational embedding models

Highlights benefits of using a distance matrix over adjacency matrices

Provides comprehensive empirical evaluation

Abstract

We consider the problem of learning distance-based Graph Convolutional Networks (GCNs) for relational data. Specifically, we first embed the original graph into the Euclidean space $\mathbb{R}^m$ using a relational density estimation technique thereby constructing a secondary Euclidean graph. The graph vertices correspond to the target triples and edges denote the Euclidean distances between the target triples. We emphasize the importance of learning the secondary Euclidean graph and the advantages of employing a distance matrix over the typically used adjacency matrix. Our comprehensive empirical evaluation demonstrates the superiority of our approach over $12$ different GCN models, relational embedding techniques and rule learning techniques.