# Leveraging Multi-Modal Information for Cross-Lingual Entity Matching across Knowledge Graphs
## 3 Method
### Entity Representation Learning in Different Views
#### 3.3.2 Attribute View  
The attribute view characterizes attribute and attribute value information of entities. There are word abbreviations in attributes and cross-lingual differences in attribute values, which make entity matching based on the attribute view quite difficult. To leverage the information of attributes and attribute values to help match entities, we use a graph convolutional network (GCN) [32] to encode the neighbour attributes and attribute values into the the low-dimensional representations of the given entities. GCN can perform feature extraction on arbitrary graphs and will not be affected by the number of neighbour nodes associated with entities.  
Firstly, we construct the entity attribute graph. All attribute triples are classified based on the head entity, i.e., attribute triples of the same head entity are grouped together. Then, for an entity \(e\), we collect all its attributes and attribute values. We combine each collected attribute and its corresponding attribute value as a neighbour node of the entity node in the entity attribute graph. Figure 2 shows an example of the entity attribute graph for the entity \"Donald Trump\".  
Secondly, we adopt GCN to encode attributes and attribute values into the representations of entities. We initialize the vector representations of entities, attributes and attribute values using the pre-training model BERT [33]. BERT is a multi-layer bidirectional Transformer encoder, and we use its original implementation, the BERT-base model. To obtain the representation of each neighbour node for the entity node in the built entity attribute graph, we perform element-wise multiplication between the vectors of attributes and attribute values, respectively. Afterwards, GCN is utilized to conduct convolution operations as follows:  
\[\mathbf{H}^{(l+1)}=ReLU(\mathbf{\hat{D}}^{-\frac{1}{2}}\mathbf{\hat{A}} \mathbf{\hat{D}}^{-\frac{1}{2}}\mathbf{H}^{(l)}\mathbf{W}^{(l+1)}) \tag{8}\]  
where \(\mathbf{H}\) denotes the feature matrix of all nodes, each row in \(\mathbf{H}\) is the vector representation of a node, \(\mathbf{A}\) is an adjacency matrix showing the connectivity between nodes, \(\mathbf{\hat{A}}=\mathbf{A}+\mathbf{I}\), \(\mathbf{I}\) is the unit matrix, \(\mathbf{\hat{D}}\) is the diagonal matrix of \(\mathbf{\hat{A}}\), \(\mathbf{W}\) is the weight matrix, and \(l\) means the \(l\)-layer. We choose \(ReLU=\max(0,x)\) for the activation function.  
Owing to the single-layer structure of the entity attribute graph, we assign a single-layer GCN for each knowledge graph to encode attributes and attribute values into the representations of entities. Specifically, given two knowledge graphs \(G_{1}\) and \(G_{2}\), the objective can be achieved by minimizing the following margin-based loss function:  
\[Loss_{attr}=\sum_{(e_{1},e_{2})\in S}[f(e_{1},e_{2})-\gamma_{1}]_{+}+\sum_{(e_{ 1}^{\prime},e_{2}^{\prime})\in S^{\prime}}[\gamma_{2}-f(e_{1}^{\prime},e_{2}^{ \prime})]_{+} \tag{9}\]  
where \([x]_{+}\) means \(max\{0,x\}\), \(f(x,y)\) means the \(L_{2}\) distance of vector \(\mathbf{x}\) and vector \(\mathbf{y}\), \((e_{1}^{\prime},e_{2}^{\prime})\) is a negative example obtained by randomly replacing one of the two entities in \((e_{1},e_{2})\) with another entity, and \(\gamma_{1/2}\) is the margin parameter describing the boundary between positive and negative examples.