Composition-based Multi-Relational Graph Convolutional Networks (1911.03082v2)

Abstract: Graph Convolutional Networks (GCNs) have recently been shown to be quite successful in modeling graph-structured data. However, the primary focus has been on handling simple undirected graphs. Multi-relational graphs are a more general and prevalent form of graphs where each edge has a label and direction associated with it. Most of the existing approaches to handle such graphs suffer from over-parameterization and are restricted to learning representations of nodes only. In this paper, we propose CompGCN, a novel Graph Convolutional framework which jointly embeds both nodes and relations in a relational graph. CompGCN leverages a variety of entity-relation composition operations from Knowledge Graph Embedding techniques and scales with the number of relations. It also generalizes several of the existing multi-relational GCN methods. We evaluate our proposed method on multiple tasks such as node classification, link prediction, and graph classification, and achieve demonstrably superior results. We make the source code of CompGCN available to foster reproducible research.

Composition-based Multi-Relational Graph Convolutional Networks

The paper "Composition-based Multi-Relational Graph Convolutional Networks" presents CompGCN, a novel extension to Graph Convolutional Networks (GCNs) specifically designed to address the complexities found within multi-relational graphs. Unlike traditional GCNs that deal with undirected graphs, this approach effectively incorporates node and relation embeddings, improving performance on a variety of essential tasks.

Overview

CompGCN is introduced as a solution to the limitations of conventional GCNs in handling multi-relational graphs, which consist of labeled and directed edges. The architecture leverages entity-relation composition operations—drawn from Knowledge Graph Embedding (KGE) techniques—to concurrently embed both nodes and relations. This joint embedding capability distinguishes CompGCN from prior models and mitigates the problem of over-parameterization, a common issue for models designed to perform in multi-relational settings.

Technical Contributions

1. Unified Embedding Framework: CompGCN accommodates a range of compositional operations derived from KGE methods, which enables the framework to jointly embed nodes and their relationships. This characteristic provides a more general and scalable approach compared to existing models.
2. Parameter Efficiency: The model introduces efficient handling of parameters through basis decomposition, thus scaling effectively with the number of relations. This efficiency is particularly exemplified when compared to the Relational GCN (R-GCN), which defines basis matrices independently for each layer.
3. Strong Performance on Multiple Tasks: The paper details robust empirical evaluations showing the superiority of CompGCN across tasks such as node classification, link prediction, and graph classification. For instance, in link prediction tasks on FB15k-237 and WN18RR datasets, CompGCN achieves top performance in most evaluated metrics.

Experimental Results

CompGCN markedly outperforms existing methods on mainstream multi-relational graph datasets. For link prediction, it showed superior performance in metrics such as Mean Reciprocal Rank (MRR) and Hits@N. The substantial gains compared to state-of-the-art methods highlight the significance of integrating relation embeddings. Furthermore, in node and graph classification tasks, CompGCN demonstrates a notable increase in accuracy, underscoring its effectiveness in diverse contexts.

• Link Prediction: For the FB15k-237 dataset, CompGCN yields an MRR of 0.355 and a Hits@10 of 0.535, outperforming other competitive baselines.
• Node Classification: On datasets such as MUTAG (Node) and AM, CompGCN improves accuracy by approximately 3% over the best existing methods.
• Graph Classification: Validations on MUTAG (Graph) and PTC datasets also show competitive results, with CompGCN excelling particularly on the PTC dataset, reflecting its strong generalized performance capabilities.

Implications and Future Developments

CompGCN’s contributions have significant implications for the theoretical and practical aspects of AI and graph-based learning:

• Theoretical Insights: By integrating multi-relational data through composed embeddings, CompGCN extends the expressive power of GCNs, opening avenues for more complex relational modeling tasks.
• Practical Applications: Given its efficient parameterization and scalability, CompGCN is well-suited for applications in various domains such as knowledge graph completion, recommendation systems, biochemical property prediction, and relational data mining.

Looking forward, future developments can further refine CompGCN by exploring more sophisticated and parameterized composition operations. Additionally, extending the framework to handle dynamic or temporal graphs could diversify its applicability and performance.

In conclusion, "Composition-based Multi-Relational Graph Convolutional Networks" introduces an impactful advancement in the landscape of graph convolutional networks. CompGCN effectively bridges the gap between traditional GCN methods and the demands of multi-relational data modeling, setting a foundation for future research in this promising direction.