Knowledge Graph Entity Alignment with Graph Convolutional Networks: Lessons Learned

The success of information retrieval in a given task critically depends on the quality of the underlying data. Another issue is that in many domains knowledge bases are spread across various data sources [20] and it is crucial to be able to combine information from different sources. In this work, we focus on knowledge bases in the form of Knowledge Graphs (KGs), which are particularly suited for information retrieval [25]. Joining information from different KGs is non-trivial, as there is no unified schema or vocabulary. The goal of the entity alignment task is to overcome this problem by learning a matching between entities in different KGs. In the typical setting some of the alignments are known in advance (seed alignments) and the task is therefore supervised. More formally, we are given graphs $G_L=(V_L,E_L)$ and $G_R=(V_R,E_R)$ with a seed alignment $A={(l_i,r_i)}_i\subseteq V_L\times V_R$. It is commonly assumed that an entity $v\in V_L$ can match at most one entity $v^{\prime }\in V_R$. Thus the goal is to infer alignments for the remaining nodes only.

In this section we review previous work for the entity alignment for Knowledge Graphs and revise datasets and current evaluation process. We believe this is useful for practitioners, since we discover some pitfalls, especially when implementing evaluation scores and selecting datasets for comparison. The overview of methods, datasets and metrics is provided in Table 1.

GCN-Align [32] is a GCN-based approach to embed all entities from both graphs into a common embedding space. Each entity $i$ is associated with structural features $h_i^s\in R^d$, which are initialized randomly and updated during training. The features of all entities in a single graph are combined to the feature matrix $H^s$. Subsequently, a two-layer GCN is applied. A single GCN layer is described by

with $\hat{A}=A+I$, where $A$ is the adjacency matrix, and ${\hat{D}}_{ii}=\sum _{j=1}^n{\hat{A}}_{ij}$ is the diagonal node degree matrix. The input of the first layer is set to $H^{\left(0\right)}=H^s$, and $\sigma$ is non-linear activation function. For the first layer, $\sigma =ReLU$, and the second layer uses the identity. The output of the second layer is considered as the structural embedding, denoted by $s_i=H_i^{\left(2\right)}\in R^d$. Both graphs are equipped with its own node features, but the convolution weights $W^{\left(i\right)}$ are shared across the graphs.

The adjacency matrix is derived from the knowledge graph by first computing a score, called functionality, for each relation as the ratio between the number of different entities which occur as head, and the number of triples in which the relation occurs

Analogously, the inverse functionality ${\alpha }_r^{\prime }$ is obtained by replacing the nominator by the number of different tail entities. The final adjacency matrix is obtained as

In addition, each entity $i$ is also equipped with attributes $h_i^a\in R^{d^{\prime }}$ which are combined into a graph attribute matrix $H^a$. Anagously, the attributes are processed by a GCN for each graph with convolution weights shared across the graphs, resulting in attribute embeddings $a_i\in R^{d^{\prime }}$.

The attribute and structure GCNs are optimized separately using SGD. As loss function, a margin-rank loss is used, exemplary for the structure embedding

where $[x{]}_{+}=max\{0,x\}$, and the margin $\gamma$ is a hyperparameter chosen separately for structure and attribute embeddings. $A_i^{-}$ denotes a set of negative samples constructed by either replacing the left or the right entity with a random entity from the same graph.

In order to compare two nodes from both graphs, the $L_1$ distance between their embeddings is used, normalised by the dimensionality.

Here, $\beta$ is a hyperparameter for the tradeoff between structural and attribute similarity.

In initial experiments we were able to reproduce the results reported in the paper using the implementation provided by the authors. Moreover, we are able to reproduce the results using our own implementation, and settings adjusted to the authors’ code. In addition, we replaced the adjacency matrix based on functionality and inverse functionality by a simpler version, where $a_{ij}=\left\{\right(h,r,t)\in T\mid h=e_i,t=e_j\}$. We additionally use ${\hat{D}}^{-1}\hat{A}$ instead of the symmetric normalization. In total, we see no difference in performance between our simplified adjacency matrix, and the authors’ one. We identified two aspects which affect the model’s performance: Not using convolutional weights, and normalizing the variance when initializing node embeddings. We provide empirical evidence for this finding across numerous datasets.

We fix using convolution weights and the variance for the normal distribution from which the embedding vectors are initialized and optimize the other hyperparameters according to validation H@1 (80/20% train-validation split) on DBP15K (JAPE) zh-en in a large-scale hyperparameter search, comprising 1,440 experiments. The hyperparameter grid is given in Table 3, and Table 4 shows the best parameters found for DBP15k (JAPE) zh-en for the four different settings. For each dataset, we perform a smaller hyperparameter search to fine-tune LR, #epochs & #layers for each dataset (again 80/20 split). Their optimal parameters are given in the appendix, in Table 6. We evaluate the best models on the official test set. Our results regarding Hits@1 (H@1), Hits@10 (H@10), mean rank (MR) and mean reciprocal rank (MRR) are summarised in Table 5.

In this work, we reported our experiences when implementing the Knowledge Graph alignment method GCN-Align. We pointed at important differences between the model described in the paper and the actual implementation and quantified their effects in the ablation study. For future work, we plan to include other methods for entity alignments in our framework.

This work has been funded by the German Federal Ministry of Education and Research (BMBF) under Grant No. 01IS18036A and by the Bavarian Ministry for Economic Affairs, Infrastructure, Transport and Technology through the Center for Analytics-Data-Applications (ADA-Center) within the framework of “BAYERN DIGITAL II”. The authors of this work take full responsibilities for its content.