SEG:Seeds-Enhanced Iterative Refinement Graph Neural Network for Entity Alignment

Translation-based entity alignment. By continuously adjusting the vector representation, the entity vector + the relation vector = the entity vector. In order to solve the shortcomings of TransE. MTransE[37] embeds entities and relations in different knowledge graphs into different vector spaces and maps them to a unified space through distance calibration and linear transformation strategies to achieve cross-knowledge graph alignment. BootEA[33] is a Bootstrap-based entity alignment method that converts entity alignment into a classification problem. It completes the alignment task by iteratively marking possible entity alignments as training data and finding the maximum possibility of alignment.

GNN-based entity alignment. GCN-align can embed entities from different KGs into a unified vector space. Embedding can be learned from the structure and attribute information of the entity. HMAN[38] embeds learning entity representation from three perspectives: structural information, relationship features, and attribute characteristics.RD-GCN[39] uses the graph attention mechanism to encourage dual relations between the interaction graph and the original graph and then feeds the vertex representation in the original graph into the GCN layer with highway neural network gating to capture the structural information of the neighbors.

The Graph Attention Network serves as a feature extraction mechanism, introducing an innovative neural network framework for processing data structured as a graph. This architecture comprises an input layer, an intermediary hidden layer, and a final output layer. Within each hidden layer, the representation of a node is determined by its interaction with the surrounding nodes’ information, necessitating ongoing updates to the hidden layer’s state. The computation is based on the following formula:

where $H_{e_{i}}^{(l+1)}$ and $H_{e_{i}}^{(l)}$ represent the embedding of the entity at the $l$ layer, $l$ represents the number of layers, and $d^{(l)}$ represents the weight parameter of the $l$ layer,$\sigma$ represents the ReLU activation function.

where $T_{ij}$ represents the set of relation triplets with $e_{i}$ as the head entity and $e_{j}$ as the tail entity, $\alpha$ is the attention parameter, $||$ are vector concatenation, $\odot$ element multiplication and LeakyReLU respectively function.

Where $T_{t}$ and $W_{t}$ represent the size of the head entity set and the tail entity set connected by $R_{t}$, respectively, $b$ is the attention parameter.

$w$ and $b$ are trainable weight matrices, and their output matrices are represented as $H_{e_{i}}$.

$Sim\in[-1,1]$, Only the similarity in the matrix $>=$ 0.95 is selected as the Candidate pre-selected set. However, these candidate sets only represent possible matching entity pairs, and there may even be one-to-many situations that cannot guarantee the accuracy of the final alignment.

Based on Entity propagate similarity. taking the aligned seeds of $KG_{1}$ and $KG_{2}$ as anchors, for any seed pair $(e_{a}^{1},e_{b}^{2})\in Align_{entity}$, we construct the neighbourhood node sets of $e_{a}^{1}$ and $e_{b}^{2}$, ${n(\bar{e}_{i}^{1})|\bar{e}_{i}^{1}\in N(e_{a}^{1})}$ and ${n(\bar{e}_{j}^{2})|\bar{e}_{j}^{2}\in N(e_{b}^{2})}$, $(e_{a}^{1},r_{a1},\bar{e}_{1}^{1})$ or $(\bar{e}_{1}^{1},r_{a1},e_{a}^{1})$. $n(\bar{e}_{i}^{1})$ represents the $i$-th neighbor node of $e_{a}^{1}$, and $r_{a1}$ represents the connection between the two. $\bar{e}_{j}^{2}$ represents the $j$-th neighbor node of $e_{b}^{2}$, $(e_{b}^{2},r_{b1},\bar{e}_{1}^{2})$, $(\bar{e}_{1}^{2},r_{b1},e_{b}^{2})$, $r_{b1}$ is the same. Here, the above cosine similarity is also used to calculate the similarity of the nodes $(e_{a}^{1},e_{b}^{2})$ in the neighborhood of the seed pair. In order to ensure that the relationship pairs screened by the neighborhood candidate alignment set are highly accurate and convenient for subsequent training, two standards are set here: First, the neighborhood alignment nodes need to meet the set $Sim_{e}$ similarity threshold and the $Match_{e}$ matching number threshold of the derived relationship. Second, we must ensure that the neighborhood nodes are aligned one-to-one. Only the neighborhood pairs with the highest similarity are selected when encountering a one-to-many or many-to-one situation.

$Sum_{1}$ represents the soft label set screened based on the entity embedding model, $Sim_{e}$ represents the cosine similarity of the neighborhood node pair, and match is the number of repetitions of the relationship between the entities. For example: $(e_{a}^{1},e_{b}^{2})\to(e_{a}^{1},r_{a1},\bar{e}_{1}^{1}),\quad(e_{b}^{2},r_{b1},\bar{e}_{1}^{2})\to\text{Sim}(\bar{e}_{1}^{1},\bar{e}_{1}^{2})>=0.98$ and $\text{Match}(r_{a1},r_{b1})>=10$,that is, keep this relationship pair in the set $Sum_{1}$.

$Sum_{2}$ represents the number of soft labels selected based on the relation embedding model, $Sim_{r}$ represents the cosine similarity of the relation pair, and $Match_{r}$ is the number of times this relation pair appears repeatedly. $\text{Sum}=\text{Sum}_{1}+\text{Sum}_{2},\quad\text{Order}(\text{Sum}_{2})>\text{Order}({Sum}_{1})$, ${Sum}_{2}$has a higher priority than ${Sum}_{2}$.

Soft labels enhance alignment precision by guiding neighborhood matching and are selectively retained based on match quality. GCN integrates this neighborhood data, while Highway networks combine entity names with neighborhood information to refine the final embeddings.

Inspired by contrastive learning, we have engineered a bidirectional weighting mechanism based on similarity aimed at optimizing the weight distribution of samples during the entity alignment process. This mechanism adjusts the weights of negative samples differentially to achieve a precise approximation of positive samples and effectively optimize negative samples. Positive samples are actual alignments $Align_{entity}$, while negative samples are selected from the top 50 nodes with the highest similarity to the positive samples in either $KG_{1}$ or $KG_{2}$. Notably, due to the most significant risk of misalignment, the node with the highest similarity is assigned the highest weight penalty.

P represents the number of positive samples, while N denotes the number of negative samples corresponding to each positive sample (n_negatives_per_positive).$D_{ij}$ represents the distance of features. The feature vector of the j-th negative sample corresponds to the i-th positive sample, where $j\in\{1,\ldots,K\}$,$\gamma$ and $\beta$ are hyperparameters.

Alignment learning. In this paper, a margin-based loss function is used. Moreover, The entity alignment training optimization in this paper adopts a semi-supervised learning method and expands the training data through an iterative strategy to reduce the dependence on manually labelled seeds and the consumption of workforce and material resources.

$[x]_{+}=\max\{0,x\},\quad(e^{1},e^{2})\in P$ represents the alignment seed positive sample set, and $e^{1}\in E^{1},\quad E^{1}\in KG_{1},\quad e^{2}$ is the same,$\quad(e^{1^{\prime}},e^{2^{\prime}})\in N$ represents the alignment seed negative sample set,$\quad D(e^{1},e^{2})=\|e^{1}-e^{2}\|_{L_{1}}$represents the $L_{1}$ function between two vectors,$\quad\gamma>0$ is a marginal hyperparameter.

DBP-15K is built on DBpedia and includes three cross-language DBpedia datasets: ZH-EN (Chinese-English), JA-EN (Japanese-English), and FR-EN (French-English).

To assess the performance of our model, we conducted comparisons against current leading entity alignment techniques. Broadly, these can be categorized as follows: Traditional Entity Alignment Methods. SEA proposes a semi-supervised entity alignment method that uses labeled entities and rich unlabeled entity information for alignment. BootEA proposes a Bootstrap-based entity alignment method. Relation-based Entity Alignment Methods. RAGA proposed a framework for capturing entity and relation interactions based on relation-aware graph attention networks. RANM[40] also demonstrates exceptional performance in leveraging relational assistance for entity alignment.

To ensure that the model remains optimal, five-fold cross-validation based on the training set (20%), validation set (10%), and test set (70%) was used, so the reported performance is the average of five independent training runs, and the training/validation/test datasets are shuffled in each round. The number of GAT layers is 2, the similarity threshold of entity embedding is 0.95, and the maximum number of neighbor nodes for alignment seeds is 982. The final training parameters are selected between the best performance period on the validation set (based on ”Hits@1”) and the last period (up to 1500 periods). The experiments were run on NVIDIA 4090 16 GB.

Our model exceeds baselines, as detailed in the table. Ablation studies adjusted parameters like GNN layers and learning rate, showing that the soft labels module enhanced DBP-15K accuracy by 0.3%-1%, especially in the ZH-EN subset with a 1% gain. Additionally, the Bidirectional Weighting module raised DBP-15K accuracy by 0.2%-0.9%, contributing to a consistent 0.7%-1.3% overall improvement across all subsets.

In assessing our model’s robustness, we tested the impact of GNN layer count and learning rate. While more GNN layers slightly lowered entity alignment accuracy but kept overall performance stable, higher learning rates (0.01, 0.005, 0.001) significantly reduced performance due to training instability and convergence challenges.