# Knowledge Graph Alignment Network with Node-Level Strong Fusion
## 4 Method
### Strong Fusion Embedding of Attribute and Structure  
In this stage, the attribute information of entities is first learned, so that nodes have alignment cues for attributes before learning structure information. Through multi-layer GCNs stacking, not only the multi-hop neighbor information of entities is learned, but also the structure and attribute alignment signals learned in each layer are transmitted to each neighbor node, to achieve strong fusion. In the first step, the information is learned by a fully-connected (FC) layer, that is considered the entity vectors initialization. The hidden representations of attribute at 0 th layer are denoted as \(h_{a}^{0}\). Then, attribute information is learned in the form of triples of <entity, attribute, attribute value>, where entities and attribute values are regarded as nodes in the graph and attribute is regarded as edges between nodes, using GCN to encode it to represent the entity by aggregating the nodes (i.e., attribute values) around the entity, denoted as \(h_{a}^{1}\), which is computed by:  
\[h_{a}^{1}=\sigma(\sum_{i\in\text{N}}W^{1}h_{a_{i}}^{0}), \tag{1}\]  
where N represents the set of all nodes connected to the central entity in the attribute graph, \(W^{1}\) denotes a learnable weight matrix, and \(\sigma\) is the Re\(LU\) function. Figure 3: Overall architecture of SFEA with two-hop neighborhood aggregation. Entity name is initialized with pre-trained English word vectors by Glove, which is denoted as \(h_{e}^{name}\). Attribute representations and entity names vectors are aggregated through highway gating mechanism. As the initial vector of the learned structure, the calculation formula is computed as follows:  
\[h_{e}^{0}=T(h_{a}^{1})\cdot h_{e}^{name}+(C(h_{a}^{1}))\cdot h_{a}^{1}, \tag{2}\]  
\[T(h_{a}^{1})=sigmoid(h_{a}^{1}W_{T}+b_{T}), \tag{3}\]  
\[C=1-T, \tag{4}\]  
where \(T\) is the transform gate that represents the proportion of the information entering the next layer after passing the GCN operation, and \(C\) is the carry gate which denotes the proportion of the information entering the next layer directly without the GCN operation. \(W_{T}\) denotes the weight matrix of the transform gate, and \(b_{T}\) denotes the bias of the transform gate. Structure information (i.e., relation triples) is also learned by taking the form of a graph. In <head entity, relation, tail entity>, head entities and tail entities are as nodes in the graph and relation as edges. Learning the entity structure via GCNs, it also transmits the alignment signal of the attribute to each node. The input for GCN layer is a node feature matrix, \(H_{e}^{0}=\left\{h_{e_{1}}^{0},h_{e_{2}}^{0},\ldots,h_{e_{n}}^{0}\left|h_{e_{i} }^{0}\in R^{d_{0}}\right.\right\}\), where n is the number of nodes of a KG, \(d^{0}\) is the number of features in 0 th layer of structure, and \(H_{e}^{0}\) denotes the 1 th layer of strong fusion and the 0 th layer of learning structure information. \(H_{e}^{1}\) is the first layer of embedded structure information and the second layer of strong fusion. In this layer, the one-hop neighborhood of entities is modeled and learned based on attribute information and entity names. Due to a central node, there are a large number of neighbor nodes associated with it. But some of neighbor nodes cannot have an effective effect on the entity alignment of a central node and have the potential to bring noise because of their diversity. Therefore, attention mechanism is added [20] to calculate the weight between entities to highlight the more important parts of the neighborhood. The calculation formula is as follows:  
\[H_{e}^{1}=\sigma(\sum_{j\in\Psi_{1}(i)}\alpha_{ij}W^{1}H_{e_{j}}^{0}+H_{e_{i}} ^{0}), \tag{5}\]  
where \(\Psi_{1}(i)\) denotes the set of one-hop neighbor entities of entity \(e_{i}\), \(\sigma\) is the Re\(LU\) function, and \(W^{1}\) is a learnable weight matrix. \[s_{ij}=v^{T}\text{tanh}(WH_{e_{j}}^{0}+q), \tag{6}\]  
where \(s_{ij}\geq 0\), \(v\), \(W\), \(q\) are learnable weight matrices.