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. However, most of the existing research on GCNs (Kipf & Welling, 2016;Hamilton et al., 2017;Veličković et al., 2018) have focused on learning representations of nodes in simple undirected graphs. A more general and pervasive class of graphs are multi-relational graphs 1 . A notable example of such graphs is knowledge graphs. Most of the existing GCN based approaches for handling relational graphs (Marcheggiani & Titov, 2017;Schlichtkrull et al., 2017) suffer from overparameterization and are limited to learning only node representations. Hence, such methods are not directly applicable for tasks that require relation embedding vectors such as link prediction. Initial attempts at learning representations for relations in graphs (Monti et al., 2018;Beck et al., 2018) have shown some performance gains on tasks like node classification and neural machine translation.
In this paper, the authors developed GCN on multi-relational graphs and proposed CompGCN. In comparison with existing multi-relational GCN, CompGCN leverages insights from knowledge graph embedding and learns representations of both nodes and relations, with the aim to alleviate the problem of over-parameterization. Moreover, to improve the scalability w.r.t. the number of relations, the initial relation representations are expressed as a linear combination of a fixed number of basis vectors. In contrast to existing works, the basis vectors are only defined for initialization but not for every GCN layer. The authors also compared the proposed CompGCN with other existing GCN variants and summarized the relationships between CompGCN and other models. In the experiments, three tasks including link prediction, node classification and graph classification were performed to evaluate the performance of the proposed method. By comparing with existing methods, the effectiveness of the proposed method was demonstrated.
There are several concerns on this paper. First, this work is somewhat incremental on R-GCN ("Modeling relational data with graph convolutional networks"). Although the differences were highlighted, the overall technical contribution is limited. In this paper, relation representations are learned jointly with node representations, but it is not clear on what are the benefits by doing so, or how significant the over-parameterization problem can be alleviated in this manner. Second, the experimental setup is unclear. As for the datasets, some more descriptions about the meaning of relationships and labels should be provided. As for the three different tasks, what loss functions were used for model training, how to obtain graph-level representations from node-level representations for graph classification, should be clarified. Third, in Table 2, there are some missing values of some compared methods, but it is not clear on their absence. Finally, from the results of Figure 3, it is hard to see the scalability of the proposed method w.r.t. the increasing number of relations since the variable is the number of basis. It is suggested to provide some more results to show the insights of advantages of the proposed method, such as the accuracy change w.r.t. increasing number of relations and the corresponding running time, in comparison with other methods.