Entity Alignment with Global Information Aggregation

Abstract

Entity alignment (EA) is a critical task in knowledge graph fusion, aiming to associate equivalent entities across disparate knowledge graphs (KGs). Current methods typically leverage entity representations derived from triples or neighboring entities, employing similarity matching for alignment. These approaches, however, tend to be overly reliant on proximal neighbor information and struggle with graph over-smoothing introduced by neighborhood aggregation. In response to these limitations, this study introduces a Global Information Aggregator (GIA), a new method that aims to enhance entity representation and simultaneously alleviate over-smoothing by merging the global structural information of the entire knowledge graph. Specifically, we propose a PageRank-based method to aggregate the global structural information of KGs. In addition, the GIA generates a diffusion-augmented graph by propagating and integrating the global information of the KGs. This graph is subsequently compared with a structural perturbation-augmented graph to yield more robust and comprehensive entity representations, thus further improving the model’s alignment performance. Extensive experiments on four benchmark datasets show that the GIA model is highly competitive with current state-of-the-art entity alignment frameworks.

1. Introduction

Knowledge graphs (KGs) are crucial in structuring and representing real-world facts, with extensive applications across diverse fields. However, single KGs have only a limited amount of information, which makes them inherently incomplete. This incompleteness compromises the capacity of a single KG to fully cater to the needs of downstream tasks, highlighting the necessity for fusing multiple KGs. A critical component of knowledge graph fusion is entity alignment, which seeks to identify and associate equivalent entities across different KGs.

Recent advancements have concentrated on embedding-based entity alignment methods [1,2,3,4,5,6,7], which have been celebrated for their superior performance. These approaches typically involve generating low-dimensional representations of entities through KG encoders and determining similarity based on aligned entity pairs. To address the challenge of over-smoothing [3,8] and enhance entity representation, recent techniques have been developed. For example, AliNet [4] uses a multi-hop aggregation strategy coupled with a gating mechanism to broaden the neighborhood scope of entities, thus enriching their representation and mitigating over-smoothing. IMEA [6] utilizes a transformer-like architecture to encode diverse structural contexts within the KGs, capturing long-range dependencies among entities. This shift from Graph Neural Networks (GNNs) [9] to transformers allows for a more nuanced representation of complex entity relationships and reduces over-smoothing. RHGN [3] suggests separating entity and relation representations to alleviate the issue of entity representation smoothness, arguing against the direct merging of relations into entity representations. Despite these advancements, challenges remain in effectively handling structured data and fully leveraging rich semantic information.

To address these obstacles, we propose the Global Information Aggregate (GIA) model for entity alignment. Our approach begins with the construction of a global information encoder that aggregates the graph’s global information, employing Graph Attention Networks (GATs) [10] to capture neighborhood structural information. To aggregate global information while minimizing over-smoothing, we adopted a PageRank-based method to create a global feature matrix. This matrix aggregates the global importance of entities and the semantic information of relations in the KGs. Recognizing the inherent asymmetry in entity relations, our model incorporates directional relation information. Moreover, we explored the application of graph diffusion [11,12] for graph augmentation in entity alignment, thereby generating semantically enriched diffusion-augmented graph through the propagation and amalgamation of global information across the knowledge graph. We further amplify the structural diversity of the knowledge graph by contrasting the graph diffusion perspective with the structural perturbation view, enabling entities to forge representations embodying both global and local semantics, thus mitigating over-smoothing and further improving the model’s alignment performance.

Overall, the main contributions of this paper are as follows:

• We propose a novel design for a global feature matrix in EA, leveraging the PageRank algorithm to aggregate global structural information and minimize over-smoothing.
• Our method introduces graph diffusion for graph augmentation in EA, creating a semantically enriched diffusion-augmented graph. This is compared with a locally-augmented graph to simultaneously consider both global and local semantics.
• Extensive experiments on the OpenEA benchmark dataset [13] demonstrate our method’s effectiveness. This validates our approach’s ability to leverage global structural information for better entity alignment.

The remaining sections of this paper are organized as follows. Section 2 reviews related work on entity alignment. Section 3 introduces the definition of the main problems addressed, and Section 4 describes the method proposed in this paper. We report the experimental results and discuss the ablation experiments and analysis in Section 5. Section 6 analyzes the limitations of our method. Finally, we conclude the paper in Section 7.

2. Related Work

2.1. Structure-Based Entity Alignment

In structure-based entity alignment, structural information is used to generate the embeddings of the KGs. Traditional embedding-based approaches have been extensively studied. For example, MTransE [1] utilizes TransE [14] as a KG encoder to embed various KGs into distinct vector spaces. These embeddings are then transformed using a designed alignment module. However, traditional models typically only consider the information within the triad and overlook the information embedded in the neighborhood structure. GNNs have a powerful structure learning capability, making them a popular choice for embedding-based entity alignment tasks. To capture neighbor information, many approaches have employed graph convolutional networks (GCNs) [15] as encoders. GCN-Align [5] was the first to utilize a GCN for capturing the neighborhood structure of entities. AliNet [4] extends the neighborhood scope using multi-hop aggregation with a gating mechanism. KE-GCN [7] combines a GCN and knowledge embedding methods to jointly capture the structural features and relational semantics of entities. IMEA [6] uses a transformer to encode neighbor information, relation triad information, and relation paths to efficiently capture long-distance dependencies between entities. This paper utilizes the structural context of the KGs to aggregate global information and generate a more comprehensive representation of entities.

2.2. Enhancement-Based Entity Alignment

Enhancement-based entity alignment aims to improve alignment modules by optimizing strategies or adding auxiliary information. Some works introduce entity names, attributes, or textual descriptions to enhance entity alignment. For instance, KDCoE [16], MultiKE [17], and RoadEA [18] introduce textual descriptions, entity names, and attribute correlation graphs, respectively, to enhance the entity alignment effectiveness. BootEA [19] uses iterative learning to find aligned entities and trains them iteratively. TEA [20] employs a pre-trained language model to model the entity alignment task as a two-way textual entailment task. MixTEA [21] was designed as an efficient integration framework to obtain reliable entity mappings for the alignment module. In this work, we refrained from adding any auxiliary information. Instead, we employ contrastive learning during the alignment process to acquire more stable entity representations.

3. Preliminaries

Knowledge graph. A knowledge graph (KG) is formalized as $G=(E,R,T)$, where E is the set of entities, R is the set of relations, and $T=\{(e,r,e^{\prime })\mid e,e^{\prime }\in E,r\in R\}$ is the set of relation triples.

Entity alignment. Given two different KGs, $G_1=(E_1,R_1,T_1)$ and $G_2=(E_2,R_2,T_2)$, entity alignment (EA) aims to find equivalent entity pairs $S=\{(e_1,e_2)\in E_1\times E_2\mid e_1\equiv e_2\}$, leveraging the embeddings of these two KGs. For better alignment results, a subset of pre-aligned entity pairs $S^{\prime }\subseteq S$ is usually provided as training data.

Graph augmentation. In this study, we used graph augmentation techniques to generate two augmented views for each original graph. We generate a diffusion-augmented graph $G^{GD}$ using the graph diffusion method and a structure perturbation-augmented graph $G^{drop}$ via random dropping.

4. Methodology

4.1. Framework

Figure 1 shows our model, which comprises three main parts. Firstly, we constructed two augmented views for each of the KGs $G_1$ and $G_2$: $G_1^{drop}$ and $G_1^{GD}$ for $G_1$, as well as $G_2^{drop}$ and $G_2^{GD}$ for $G_2$. Next, embedding module B is utilized to process multiple structural contexts (global features, neighborhood information, and relation directions) to generate comprehensive entity embeddings. Contrastive learning is then used to compare the graph diffusion view and structural perturbation view of the two KGs. Finally, the contrast loss and entity alignment loss are jointly optimized. In the following sections, we provide a detailed description of each section.

4.2. Graph Augmentation

Graph improvement refers to the modification and enhancement of graph structures to improve a model’s ability to understand and process graph-based information. Although various graph improvement methods [12,22] have been investigated in existing research, their applicability to entity alignment tasks remains selective. Our work focused on the effective utilization of graph improvement to facilitate contrastive learning in entity alignment tasks. We aimed to enrich the structural information of KGs from different perspectives.

4.2.1. Graph Diffusion

Figure 2 shows a diffusion-augmented graph in the improvement module. The graph diffusion improvement is employed to aggregate additional global information via global probability transfer, effectively addressing the over-smoothing challenge [8] and integrating long-distance neighborhood data by facilitating propagation throughout the graph.

The graph diffusion enhances the graph’s information using the Personalized PageRank (PPR) algorithm [11]. The PPR algorithm calculates node importance by simulating a random walk process starting from the central entity and returning to it with a certain probability in each step. This method utilizes the graph’s topology and emphasizes the significance of various entity relations by adjusting the probability of random walks. It strikes a balance between retaining the original graph information and aggregating information from distant neighbors. The graph diffusion process is defined as follows:

$$S={\mathsf{\Sigma }}_{k=0}^{\infty }{\theta }_k{T}^K,$$

(1)

where ${\theta }_k$ is a parameter used to control the distribution of local and global signals, and $T\in R^{E\times E}$ is the transfer adjacency matrix. The PPR implements graph diffusion by defining the parameter $T=D^{-1/2}A{D}^{-1/2}$ and ${\theta }_k=\alpha {(1-\alpha )}^k$, where A is the adjacency matrix, D is the degree matrix, and $D^{-1/2}$ is used to normalize the adjacency matrix so that a random walk becomes a probabilistic process. Therefore, Equation (1) can be redefined as

$$S=\alpha {(I-(1-\alpha )D^{-1/2}A{D}^{-1/2})}^{-1},$$

(2)

where $\alpha \in (0,1)$ is an adjustable parameter in the random walk controlling the teleportation probability, and I is the unit matrix. After KG diffusion through the PPR, a dense diffusion matrix is generated, representing the similarity between any pair of nodes. To further enhance the graph’s structure and increase its sparsity, we apply a threshold after the diffusion, setting elements below this threshold to zero. This strategic approach not only focuses on highly similar nodes but also reduces noise and computational load by eliminating connections with lower similarity values. Finally, a graph augmented with diffusion is generated to enhance entity alignment.

4.2.2. Structural Perturbation

To enhance the knowledge graph without introducing erroneous facts, we employed random dropout instead of operations that might introduce data errors, such as adding new nodes or replacing edges. Specifically, we randomly removed a certain proportion of triplets from the knowledge graph during each training iteration, with the dropout rate ranging from 0 to p, where p is a pre-defined threshold. To prevent the generation of isolated nodes in the enhanced graph, entities with degrees less than 2 were retained during the random dropout process [23]. By randomly deleting triplets from the knowledge graph, we simulate scenarios of information loss, thereby encouraging the model to learn more robust local structural representations.

As shown in Figure 1, we applied diffusion and perturbation augmentation separately to two knowledge graphs, resulting in their respective improved graphs. Our model can now learn global information from the graph diffusion-augmented view and local information from the structural perturb-augmented view through contrastive learning.

4.3. KG Encoder

In Figure 1B, the module illustrates our advanced KG encoder, which was designed to integrate multiple structural contexts, thereby generating embeddings that fuse global information from the KGs. Specifically, a GAT is used to aggregate neighborhood information around entities. Additionally, we transform relational triples within the knowledge graph into relational feature matrices. These matrices are further enriched with global information through our novel PageRank-based method, enhancing the overall knowledge graph embeddings. Considering the inherent asymmetry in entity relations, our method accounts for both direct relations and their inverses. This strategy facilitates a thorough understanding of the semantic information embedded within relations. By integrating these three dimensions of structural information, our encoder adeptly captures not only the local structural nuances of entities but also their global significance and the semantic depth of the relations. This complex approach ensures the generation of rich and expressive embeddings.

4.3.1. Neighborhood Encoding

Firstly, we aggregate the neighborhood information of entities through a structural encoder. This approach is based on the structural assumption that equivalent entities in different knowledge graphs often have similar neighborhood structures [5]. To achieve this goal, we utilize a GAT to aggregate neighborhood information. Specifically, the hidden layer $h_i$ can be obtained by aggregating information from the one-hop neighbors of the central entity. The GAT employs attention mechanisms to learn the importance of the different neighbors of the central entity, allowing the model to weigh each neighbor’s importance when aggregating neighborhood information. By stacking multiple layers of GATs, we can capture and integrate information from neighbors at different scopes, thereby obtaining a more comprehensive neighborhood context

$$h_i=ELU\left({\mathsf{\Sigma }}_{e_j\in N_i}{a}_{ij}{h}_j\right),$$

(3)

where $a_{ij}$ represents the importance of a surrounding entity $e_j$ with respect to the central entity $e_i$, which is computed using self-attention:

$$a_{ij}=\frac{exp\left(LeakyReLU\left(a^{\top }[W{h}_i\Vert W{h}_j]\right)\right)}{{\mathsf{\Sigma }}_{k\in N_i}\left(LeakyReLU\left(a^{\top }[W{h}_i\Vert W{h}_j]\right)\right)},$$

(4)

where ‖ denotes the concatenation operation, $\alpha$ and W represent shared learnable parameters, and $h_i$ and $h_j$, respectively, denote the embedding of entities $e_i$ and $e_j$.

In practice, a two-layer Graph Attention Network (GAT) is utilized to aggregate local structural information. Subsequently, a K-heads independent attention mechanism, where $K=2$, is employed to derive the final structural embedding $h_i^L$. This embedding is obtained by concatenating the features from each head as follows:

$$h_i^L={\oplus }_{k=1}^K\mathrm{LeakyReLU}\left(\sum _{j\in N\left(i\right)}{a}_{ij}^k{h}_j\right),$$

(5)

where $a_{ij}^k$ represents the normalized attention coefficient computed by the k-th head, as determined by Equation (4).

4.3.2. Relation Encoding

The relation direction carries rich information, but KGs are normally unidirectional. Following prior work [3,4,24], we not only consider relation information in the encoding but also add inverse relations to the KGs to capture rich relation semantic information through relation direction. Specifically, based on the in-degree and out-degree of entities in KG relation triplets, we construct sets of forward relations and inverse relations to represent hidden relation semantic information. We then average their embedding separately and concatenate them together:

$$h_{e_i}=\frac{1}{\mid N_{e_i}^{+}\mid }{\mathsf{\Sigma }}_{r\in N_{e_i}^{+}}{h}^r\Vert \frac{1}{\mid N_{e_i}^{-}\mid }{\mathsf{\Sigma }}_{r\in N_{e_i}^{-}}{h}^r,$$

(6)

where $\mid N_{e_i}^{+}\mid$ represents the set of forward relations for entity $e_i$, and $\mid N_{e_i}^{-}\mid$ represents the set of inverse relations for entity $e_i$.

4.3.3. Global Feature Encoding

The phenomenon of over-smoothing, a common challenge in the stacking of multi-layer networks within GNN models, significantly hampers the model’s ability to distinguish between entity features as the network depth increases. To address this issue, we drew inspiration from existing methodologies [12,25] for processing KG relation triplets. Specifically, we transform triplet information into feature matrices, aiming to leverage the comprehensive information embedded within the entire graph. Our approach uses the PageRank algorithm to evaluate the relative importance of each entity in the entire KG. This method is beneficial to integrating KG global entity information into the construction of feature matrices.

Firstly, we recognize that KGs contain a wealth of information among entities, which is crucial for understanding the semantics of these entities. The significance of each relation within the KG is quantified by evaluating its frequency. Subsequently, we compute the PageRank score for every entity within the knowledge graph. This score serves as a global indicator of an entity’s importance, enriching the relations’ feature matrix with insight into the relative importance of each entity within the overall graph and the importance of its relations. The implementation of the PageRank method follows its classical formulation, which is articulated as follows:

$$PR\left(u\right)=\frac{(1-d)}{N}+d{\mathsf{\Sigma }}_{v\in B_U}\frac{PR\left(v\right)}{L\left(v\right)},$$

(7)

where $PR\left(u\right)$ represents the PageRank score of node u, d is the damping factor signifying the probability of continuing the random walk at each step by randomly transitioning to the next node along the outgoing links of the current graph, $B_u$ denotes the set of in-degrees of node u, and $L\left(v\right)$ is the number of out-degrees of node v. Figure 3 shows the global feature encoding in the KG encoder module. The weighting of an entity within the KG is refined using the PageRank scores of the entities involved. This innovative weighting scheme prioritizes relations linked to entities of higher significance—those with elevated PageRank scores—thereby assigning them enhanced weights in the feature matrix. During the training of entity alignment models, this enriched feature matrix facilitates a more nuanced consideration of entity relations. It not only accounts for the direct connections between entities but also capitalizes on the relative standings and importance of entities across the entire KG. Consequently, this strategy culminates in the generation of a feature vector for each entity, containing the frequencies of its most pivotal relations alongside global importance scores.

To synthesize a comprehensive representation of each entity, we amalgamate three key aspects: the neighborhood structure, global features within the KGs, and the semantics of its relations. This amalgamation yields a rich and multifaceted output representation for each entity, which is integrated into the KG encoder. In the subsequent training process, the two knowledge graphs are embedded through the KG encoder, denoted as $h_1^{drop}$ and $h_2^{drop}$ for representations generated using structural perturbation-augmented and $h_1^{GD}$ and $h_2^{GD}$ for representations generated using the graph diffusion improvement.

4.4. Model Training

In this section, we will introduce the two losses we utilized: margin-based alignment loss and contrastive learning loss. We employed joint contrastive learning to learn entity representations that are more robust and contain richer information.

4.4.1. Margin-Based Alignment

We applied margin-based alignment loss [4,5,23] by minimizing the loss function to make the distance between aligned entities as close as possible while pushing unaligned entities apart from each other. This loss function is defined as

$${\mathcal{L}}_{align}={\mathsf{\Sigma }}_{(e_1,e_2)\in S}{\mathsf{\Sigma }}_{(e_1^{\prime },e_2^{\prime })\in S^{\prime }}[\Vert h_{e_1}^{drop}-h_{e_2}^{drop}{\Vert }_{L_2}+\lambda -\Vert h_{e_1^{\prime }}^{drop}-h_{e_2^{\prime }}^{drop}{{\Vert }_{L_2}]}_{+},$$

(8)

where $\lambda$ is a margin hyper-parameter, ${\left[x\right]}_{+}=max\{0,x\}$ ensures that the output is non-negative, S is the set of pre-aligned entity pairs, $S^{\prime }$ is the set of negative samples generated using the truncated negative sampling strategy, and $\Vert •\Vert$ represents the $L_2$ distance. To further focus on local information and prevent overfitting, we used embedding $h^{drop}$ generated through the structural perturbation augmentation in the margin-based alignment loss. This not only strengthens the model’s ability to capture local structural information but also enhances generalization to unseen data by randomly dropping some information.

4.4.2. Contrastive Learning

Contrastive learning has been widely utilized in graph representation learning [12,22,26], allowing for the promotion of heterogeneous representations of entities through contrasting different enhanced views, which can be applied to entity alignment tasks. While the GAEA [23] leverages contrastive learning to improve entity alignment, it primarily contrasts the original KGs with an enhanced version, thus not fully exploiting the potential of comprehensive global structural information. To address this, our work introduces graph diffusion improvement, a strategy adept at capturing the global structural intricacies of KGs, thereby augmenting the graph improvement process. In optimizing the consistency between local (structural perturbation-augmented view) and global (graph diffusion view) structural representations, our model concurrently assimilates both global features and local feature information of the KGs.

As shown in the Figure 1C module, we perform contrastive learning, where the contrastive loss between the graph diffusion view $G_{e_i}^{GD}$ and the structural perturbation-augmented view $G_{e_i}^{drop}$ of entity $e_i$ is defined as

$${\mathcal{L}}_{contrast}(G_{e_i}^{drop},G_{e_i}^{GD})=-log\frac{exp(sim(proj\left(h_{e_i}^{drop}\right),proj\left(h_{e_i}^{GD}\right))/\tau )}{{\mathsf{\Sigma }}_{e_k\in E}exp(sim(proj\left(h_{e_i}^{drop}\right),proj\left(h_{e_i}^{GD}\right))/\tau )},$$

(9)

where $sim(•)$ utilizes cosine similarity as the similarity measure, $\tau$ is a temperature parameter used to scale the similarity scores, and $proj(•)$ consists of linear layers, normalization layers, and ELU activation functions to map the entity representations generated by the KG encoder to a low-dimensional vector space. Similarly, the contrastive loss from $G_{e_i}^{GD}$ to $G_{e_i}^{drop}$ can be defined in the same manner. The final contrastive loss is the average of these two parts of the loss:

$${\mathcal{L}}_{contrast}={\mathsf{\Sigma }}_{z=\{1,2\}}\frac{1}{2|E_z|}{\mathsf{\Sigma }}_{e_i\in E_z}({\mathcal{L}}_{contrast}(G_{e_i}^{drop},G_{e_i}^{GD}),{\mathcal{L}}_{contrast}(G_{e_i}^{GD},G_{e_i}^{drop})$$

(10)

4.4.3. Objectives

Finally, we combine the margin-based alignment loss with the contrastive losses from the two graphs to obtain our final optimization objective:

$$\mathcal{L}={\mathcal{L}}_{align}+\beta {\mathcal{L}}_{contrast},$$

(11)

where $\beta$ is a tunable parameter used to balance the relative importance of these two types of objectives.

4.5. Inference

After enhancing two knowledge graphs and obtaining entity representations through embedding methods, we can infer the alignment relation between entities in the two knowledge graphs by measuring the distance between entities. In this work, we adopted the Euclidean distance as the metric. Specifically, to find the aligned entity of entity $e_i$ in $G_1$, we traverse all entities in $G_2$ and use the nearest neighbor algorithm to search for the entity closest to $e_j$:

$$e_j=argmi{n}_{e_k\in G_2}{\Vert h_{e_i}-h_{e_k}\Vert }_{L_2}$$

(12)

Through this approach, we can find a best-matching aligned entity for each entity in $G_1$, thereby constructing alignment relations between the two knowledge graphs.

5. Experiments

5.1. Datasets

We evaluated our method on the OpenEA 15k benchmark dataset (V1) [13] because it conforms to the data distribution of real-world knowledge graphs. This dataset comprises four sub-datasets, including two cross-lingual datasets, namely, EN-FR-15K (English-French) and EN-DE-15K (English-German), as well as two monolingual datasets, namely, D-W-15K (DBpedia to Wikidata) and D-Y-15K (DBpedia to YAGO). In

Table 1. Statistics of OpenEA datasets.

Dataset	KG	#Ent.	#Rel.	#Tri.
EN-FR-15K	English	15,000	267	47,334
	French	15,000	210	40,864
EN-DE-15K	English	15,000	215	47,676
	German	15,000	131	50,419
D-W-15K	DBPedia	15,000	248	38,265
	Wikidata	15,000	169	42,746
D-Y-15K	DBPedia	15,000	165	30,292
	YAGO	15,000	28	26,638

, we provide detailed information about OpenEA. We followed the data splitting approach in OpenEA, where 20% of entity pairs are used for training, 10% for validation, and 70% for testing.

5.2. Implementation Details

Our GIA model was implemented using the PyTorch framework. The trainable parameters in the model were initialized using the Xavier initializer, ensuring a reasonable distribution of parameters at the beginning of the training. We optimized the loss function using the Adam optimizer. As for hyper-parameters, the learning rate was set to 0.001, the number of layers L in the GAT was set to 2, the number of negative samples per entity was set to 5 to enhance the model’s discriminate ability, the margin $\lambda$ was set to 1, and triplet embeddings were set to 256, 128, and 256 respectively. The initial value of the dropout was uniformly set to 0.2. In the KG encoder, the damping factor for the PageRank algorithm used in the global feature encoding was set to the default value of 0.85. For the damping factor in graph diffusion enhancement, we employed a grid search method to determine the optimal value from the set {0.05, 0.15, 0.25, 0.35, 0.45}. The graph diffusion parameter is set to 0.0001, and the initial value of p for graph perturbation enhancement was set to 0.1.

To comprehensively evaluate the model performance, we employed five-fold cross-validation and report the average experimental results. The evaluation metrics included Hits@1, Hits@5, and MRR, where Hits@k measures alignment accuracy and MRR reflects the average ranking of correct answers. We performed early stopping based on the MRR performance tested on the validation set every 10 epochs to terminate training. By default, the alignment direction was from left to right; for example, in the D-Y-15K dataset, our goal was to find aligned entities on YAGO corresponding to entities on DBpedia.

5.3. Baseline Method

To comprehensively evaluate the effectiveness of the GIA model, we extensively compared it with the current state-of-the-art entity alignment methods, including MTransE [1], AlignE [19], and SEA [27], which focus on utilizing direct entity and relation triplet local information for alignment; GCN-Align [5], AliNet [4], HyperKA [28], and KE-GCN [7], which enhance entity representations by aggregating neighborhood information through GNN; and IPTransE [29], RSN4EA [2], and other methods that capture distant dependencies between entities through relation paths. Additionally, we compared our method with some recently proposed strong baselines such as IMEA [6], GAEA [23], and RHGH [3] to further demonstrate the superiority of our model.

To ensure fairness in the comparison, we focused on methods that primarily utilize KG structural information and exclude those relying on auxiliary information (such as attributes, entity names, and descriptions), such as RoadEA [18] and TEA [20]. Such settings aim to accurately assess the performance of each model in utilizing structural information for entity alignment tasks, thus clearly demonstrating the contributions and advantages of our GIA.

5.4. Experimental Results

Table 2. Entity alignment results on OpenEA datasets.

Models	EN-FR-15K			EN-DE-15K			D-W-15K			D-Y-15K
	Hit@1	Hit@5	MRR	Hit@1	Hit@5	MRR	Hit@1	Hit@5	MRR	Hit@1	Hit@5	MRR
GCN ‡	0.210	0.414	0.304	0.304	0.497	0.394	0.208	0.367	0.284	0.343	0.503	0.416
GAT ‡	0.297	0.585	0.426	0.542	0.737	0.630	0.383	0.622	0.489	0.468	0.707	0.573
MTrans †	0.247	0.467	0.351	0.307	0.518	0.407	0.259	0.461	0.354	0.463	0.675	0.559
IPTrans †	0.169	0.320	0.243	0.350	0.515	0.430	0.232	0.380	0.303	0.313	0.456	0.378
AlignE †	0.357	0.611	0.473	0.552	0.741	0.638	0.406	0.627	0.506	0.551	0.743	0.636
SEA †	0.280	0.530	0.397	0.530	0.718	0.617	0.360	0.572	0.458	0.500	0.706	0.591
GCN-Align †	0.338	0.589	0.451	0.481	0.679	0.571	0.364	0.580	0.461	0.465	0.626	0.536
HyperKA *	0.353	0.630	0.477	0.560	0.780	0.656	0.440	0.686	0.548	0.568	0.777	0.659
RSN4EA †	0.393	0.595	0.487	0.587	0.752	0.662	0.441	0.615	0.521	0.514	0.655	0.580
AliNet *	0.364	0.597	0.467	0.604	0.759	0.673	0.440	0.628	0.522	0.559	0.690	0.617
KE-GCN *	0.408	0.670	0.524	0.658	0.822	0.730	0.519	0.727	0.608	0.560	0.750	0.644
IMEA ∘	0.458	0.720	0.574	0.639	0.827	0.724	0.527	0.753	0.626	0.639	0.804	0.712
GAEA∘	0.486	0.746	0.602	0.684	0.854	0.854	0.562	0.768	0.654	0.608	0.791	0.688
RHGH ∘	0.500	0.739	0.603	0.704	0.859	0.771	0.560	0.753	0.644	0.708	0.831	0.762
GIA	0.507	0.758	0.619	0.684	0.859	0.760	0.572	0.774	0.662	0.737	0.869	0.796

reports the comparison of entity alignment performances on the OpenEA 15k dataset [13]. Results marked with † are from OpenEA, while those marked with * are from [6], those marked with ‡ are from [23], and those marked with ∘ are from their respective reference papers. In the table, bold numbers indicate the best result for each column, while numbers underlined represent the second-best result. These results demonstrate that our GIA model exhibits a superior performance on most datasets compared to existing SOTA baseline models, primarily relying on structural information. In particular, in the same language environment, our method outperforms the best-performing baselines (i.e., RHGN, IMEA) by 1–3% in Hits@1, 0.8–3.4% in MRR, and 0.6–3.8% in Hits@5. Although our performance on the EN-DE-15K dataset was slightly lower than that of the RHGN model by 1.1–2%, this is mainly because RHGN addresses heterogeneity by distinguishing entities and relations and employs cross-graph exchange and soft relation alignment strategies. However, RHGN fails to consider distant entity information, and its performance heavily depends on the accuracy of automatically generated soft relation alignment labels, leading to poor performances on other datasets.

Further analysis revealed that methods like AliNet and IMEA, which utilize distant graph information, generally yield superior results, affirming the value of incorporating distant information. Moreover, the runtime comparison of the models in

Table 3. Comparison of execution times for models.

Models	Times (s)
AliNet	367
IMEA	479
GIA (ours)	415
w/o Global feature	355
w/o GD	372
w/o Global feature + GD	293

shows that the GIA model, while consuming an amount of time to comparable to those of IMEA and AliNet, achieves significant enhancements in entity alignment by effectively aggregating distant information. Overall, the GIA model advances entity alignment capabilities by refining graph entity representations, thereby demonstrating its robustness and superiority across various knowledge graph datasets.

5.5. Efficiency and Ablation Study

In this section, we demonstrate the efficacy of the global information aggregate (GIA) model’s components via ablation studies, with the findings presented in Table 3 and

Table 4. Ablation study results.

Methods	EN-FR-15K		EN-DE-15K		D-W-15K		D-Y-15K
	Hits@1	MRR	Hits@1	MRR	Hits@1	MRR	Hits@1	MRR
GIA	0.507	0.619	0.684	0.760	0.572	0.662	0.737	0.796
w/o Global feature	0.501	0.613	0.676	0.754	0.570	0.660	0.718	0.782
w/o GD	0.498	0.611	0.675	0.754	0.568	0.658	0.668	0.736
w/o Global feature + GD	0.484	0.599	0.673	0.750	0.557	0.650	0.606	0.688

. The experimental setup was as follows:

• w/o Global feature: This variant removes the global feature matrix from the encoder to evaluate the influence of a global feature on the model performance.
• w/o GD: This variant uses the original graph instead of the diffusion-enhanced graph in the contrastive learning process, aiming to evaluate the contribution of the diffusion improvement to the model performance.
• w/o Global feature + GD: This setup simultaneously removes both the global feature encoding and the diffusion-enhanced graph to explore the combined effect of these enhancement strategies on the model performance.

Considering that our proposed method is based on the PageRank algorithm, which is a graph-based random walk model, we studied and compared the execution time of our model on the D-W-15K dataset and conducted ablation experiments on the runtime, as shown in Table 3. Since the execution times of these methods are not disclosed, we conducted the experiments in the same environment, maintaining the default parameters for these methods. IMEA [6] utilizes a transformer to perform random walks to aggregate global information. Similarly, we used PageRank for random walks; however, to ensure execution efficiency, we processed the graph into a sparse graph.

The experimental results indicate a performance decrement across all three variants compared to the baseline GIA model. The significant performance drop upon removing the global feature encoding from the encoder highlights the critical importance of integrating global information from relation feature matrices for entity alignment tasks. Moreover, the notable performance decline when replacing the diffusion-enhanced graph with the original graph underscores the utility of diffusion-enhanced views in entity alignment tasks. This implies that by contrasting diffusion views with dropout views, the model can effectively encode both local and global information, thus yielding more comprehensive and stable entity representations. The outcomes of the third variant further validate that the simultaneous exclusion of these two enhancement strategies has the most detrimental impact on model performance. These variants support our hypothesis that the incorporation of global information significantly enhances the model’s expressive power, emphasizing the necessity of both strategies for entity alignment tasks, with the graph diffusion improvement having a more substantial effect on improving model performance. Therefore, the results of the ablation studies underline the indispensability of relation triplet information and the graph diffusion improvement strategy in the GIA model, demonstrating their vital roles in boosting the entity alignment performance.

The ablation experiment results shown in Table 4 illustrate that both graph diffusion enhancement and global feature encoding consume additional time. However, as shown in Table 3, when these two components are removed, the execution time is less than those of general methods while still ensuring acceptable results.

5.6. Analysis of Over-Smoothing

To validate that our model can alleviate the over-smoothing issue in knowledge graphs, we followed the work of PAIRNORM [30] and quantified over-smoothing using the row-diff metric. The row-diff metric measures the average of all pairwise distances between node features (i.e., the rows of the representation matrix) and quantifies the over-smoothing between nodes. This metric is also applicable in assessing over-smoothing issues in the embeddings of entity alignment models. Let $H\left(k\right)\in {\mathbb{R}}^{n\times d}$ be the representation matrix after k graph convolutions. Let $h_i^{\left(k\right)}\in {\mathbb{R}}^d$ be the i-th row of $H\left(k\right)$ and $h_i^{\left(k\right)}\in {\mathbb{R}}^n$ be the i-th column of $H\left(k\right)$. Then, we define row-diff($H\left(k\right)$) as follows:

$$\text{row-diff}\left(H\left(k\right)\right)=\frac{1}{n^2}\sum _{i,j\in \left[n\right]}{∥h_i^{\left(k\right)}-h_j^{\left(k\right)}∥}^2$$

(13)

As the number of graph convolutional layers (k) increases, the graph neural network mixes the node representations with those of their neighbors, making them difficult to distinguish and leading to over-smoothing. In Figure 4, we ran the GIA and GAT on the D-W-15K dataset (DBpedia to Wikidata) for 500 epochs and observed that our model’s row-diff is higher than the GAT’s by approximately 1-2 times, providing supporting evidence that our model can alleviate over-smoothing in knowledge graphs.

5.7. Analysis of Graph Diffusion

To analyze the impact of the graph diffusion algorithm on our model, we examined how changes in the damping factor affected performance on the D-W-15K and EN-DE-15K datasets. As shown in Figure 5(right), on the D-W-15K dataset, the model’s performance improved with increasing damping factor values, peaking at 0.15. This suggests that entities in D-W-15K benefit from incorporating information from distant neighbors, which enhances the quality of their representations. In contrast, the impact of graph diffusion on the EN-DE-15K dataset was less pronounced, as most models already performed well. This difference likely arises because, for entities in EN-DE-15K, inherent node information and the local structure are more crucial than distant neighbor information in shaping representations. Thus, the performance gains from graph diffusion were not as significant on this dataset as on others. These findings highlight the global information aggregate (GIA) model’s ability to enhance entity representations through aggregating global information.

6. Limitations

Despite the promising results of the GIA on four real-world datasets, there are still limitations that require further investigation. Firstly, our experimental results indicate that aggregating global information can significantly enhance the performance. However, since we utilize information from the entire graph, our model demands additional computational resources and time. Therefore, it is worth exploring how to reduce the required extra computational resources and time while aggregating global information.

7. Conclusions

In this paper, we introduced the global information aggregate (GIA) model, designed to leverage the comprehensive information of entire KGs for generating enriched entity representations, thereby mitigating the issue of over-smoothing often encountered in graph-based models. Initially, we developed a global feature matrix aimed at aggregating the KG’s global structural information, facilitating the generation of information-dense entity representations while addressing the over-smoothing challenge inherent in neighborhood aggregation. Subsequently, we integrated graph diffusion techniques into the entity alignment task, empowering the model to assimilate and learn from the expansive context of the KG’s global information. Furthermore, by contrasting the graph diffusion view with the structural perturbation view within the same KGs, we achieved more stable and detailed entity representations for the entity alignment task. The efficacy of our proposed approach was substantiated through extensive experiments conducted on four real-world datasets.