Entity alignment method for aeronautical metrology domain based on multi-perspective entity embedding
基于多视角实体嵌入的航空计量领域实体对齐方法

Aeronautical metrology航空计量学
Entity alignment实体对齐
Entity embedding实体嵌入
Knowledge graph知识图谱

Aviation metrology is crucial in the aviation industry, significantly impacting aircraft design, manufacturing, testing, and maintenance. Metrology is foundational for ensuring product quality by maintaining consistent, accurate, and effective performance parameters throughout the product’s lifecycle, enabling it to perform its intended tasks at any given time reliably. Given the stringent reliability and safety demands of aviation products, meticulous measurement, calibration, and management of each performance parameter are essential to maintain optimal aircraft conditions during operation [1,2].
航空计量在航空工业中至关重要，对飞机设计、制造、测试和维护有着显著影响。计量是确保产品质量的基础，通过在产品生命周期内保持一致、准确和有效的性能参数，使其能够在任何时刻可靠地执行预定任务。鉴于航空产品对可靠性和安全性的严格要求，必须对每个性能参数进行细致的测量、校准和管理，以确保飞机在运行中的最佳状态[1,2]。

With advancements in aviation technology, modern aircraft have significantly improved in function and performance, accompanied by increased complexity. The metrological traceability system, crucial for monitoring aircraft performance, has expanded to encompass the transfer of metrology parameter values across aviation products, parameters, test equipment, calibration equipment, and metrology standards [3,4]. However, data supporting the safe and reliable operation of aircraft suffer from issues such as heterogeneity, ambiguity, and redundancy arising from multiple sources. These data are typically dispersed among metrological traceability manuals and product design
随着航空技术的进步，现代飞机在功能和性能上有了显著提升，同时复杂性也随之增加。计量溯源系统作为监测飞机性能的关键，已扩展到涵盖航空产品、参数、测试设备、校准设备及计量标准之间计量参数值的传递[3,4]。然而，支持飞机安全可靠运行的数据存在异构性、模糊性和冗余性等问题，这些问题源于多种数据来源。这些数据通常分散在计量溯源手册和产品设计中。
specifications, leading to data islands due to varying formats across departments and a lack of standardized data naming conventions. Current practices in aviation product metrology heavily rely on historical manual queries and professional empirical knowledge. However, the sharing and reuse of metrological knowledge face challenges due to the prevalence of isolated and ambiguous data. This study aims to integrate heterogeneous metrological traceability data from diverse sources to eliminate ambiguity and redundant information. The goal is to establish a unified and standardized aeronautical metrological knowledge system that offers high-quality support for the digitized metrology processes of aeronautical products.
规范不统一，导致各部门因格式差异产生数据孤岛，且缺乏标准化的数据命名规范。当前航空产品计量实践高度依赖历史手工查询和专业经验知识。然而，由于数据孤立且含糊，计量知识的共享和复用面临挑战。本研究旨在整合来自多源的异构计量溯源数据，以消除歧义和冗余信息。目标是建立统一标准的航空计量知识体系，为航空产品数字化计量过程提供高质量支持。

In recent years, the burgeoning fields of big data and artificial intelligence have facilitated the widespread adoption of knowledge graph (KG) across various domains, including healthcare and geography [5,6]. This technology has also introduced innovative approaches to the aviation industry. The aeronautical metrology knowledge graph (AMKG) organically organizes the concepts and their relationships in the metrology traceability system in the form of a graph structure, which lays the foundation for the construction of an intelligent system of aviation metrology [7]. Multi-source heterogeneous aeronautical metrology data will form multiple knowledge graphs for different
近年来，蓬勃发展的大数据和人工智能领域促进了知识图谱（KG）在包括医疗保健和地理学等多个领域的广泛应用[5,6]。该技术还为航空业引入了创新的方法。航空计量知识图谱（AMKG）以图结构的形式有机地组织了计量溯源系统中的概念及其关系，为构建智能航空计量系统奠定了基础[7]。多源异构的航空计量数据将形成多个针对不同领域的知识图谱。

scenarios, and there is a large amount of overlapping and complementary knowledge between these knowledge graphs. Knowledge fusion integrates disparate knowledge across multiple knowledge graphs [8,9]. A crucial component of this process, entity alignment (EA), involves determining the equivalence of entities across different knowledge graphs $[10,11]$$[10,11]$[10,11][10,11]. The precision of entity alignment significantly impacts the construction quality of AMKG and, in turn, affects the metrology reliability of aviation products.
场景之间存在大量重叠和互补的知识，这些知识分布在多个知识图谱中。知识融合整合了跨多个知识图谱的不同知识[8,9]。这一过程的关键组成部分是实体对齐（EA），即确定不同知识图谱中实体的等价性 $[10,11]$$[10,11]$[10,11][10,11] 。实体对齐的准确性显著影响 AMKG 的构建质量，进而影响航空产品的计量可靠性。

Entity alignment methods are typically categorized into three types: similarity-based, knowledge graph embedding-based, and graph neural network-based. These methods have demonstrated effectiveness in aligning entities across cross-lingual knowledge graphs [12-14]. However, the entity alignment of AMKG presents distinct challenges that differ from those encountered in cross-lingual KGs. 1) AMKG encompasses numerous homonymous entities that necessitate differentiation through structural embedding. 2) AMKG features a variety of $1-\mathrm{N},\mathrm{N}-1$$1-\mathrm{N},\mathrm{N}-1$1-N,N-11-\mathrm{N}, \mathrm{N}-1, and N-N metrological traceability relationships, requiring differentiation via relational embedding. 3) The entities in AMKG also possess extensive and significant attribute information, which demands distinction through attribute embedding. To address these challenges, this paper presents an entity alignment method tailored for the aeronautical metrology domain, based on a multi-perspective entity embedding approach. The main contributions of this study are summarized as follows:
实体对齐方法通常分为三类：基于相似度的、基于知识图谱嵌入的和基于图神经网络的。这些方法已在跨语言知识图谱的实体对齐中展现出有效性[12-14]。然而，航空计量知识图谱（AMKG）的实体对齐面临着与跨语言知识图谱不同的独特挑战。1）AMKG 包含大量同名实体，需要通过结构嵌入进行区分。2）AMKG 具有多种 $1-\mathrm{N},\mathrm{N}-1$$1-\mathrm{N},\mathrm{N}-1$1-N,N-11-\mathrm{N}, \mathrm{N}-1 和 N-N 计量溯源关系，需通过关系嵌入加以区分。3）AMKG 中的实体还拥有丰富且重要的属性信息，需通过属性嵌入进行区分。为应对这些挑战，本文提出了一种基于多视角实体嵌入的航空计量领域实体对齐方法。本研究的主要贡献总结如下：

Entity alignment is a crucial task in knowledge fusion, primarily involving three methodologies: similarity-based, knowledge graph embedding-based, and graph neural network-based methods.
实体对齐是知识融合中的一项关键任务，主要涉及三种方法：基于相似度的方法、基于知识图谱嵌入的方法和基于图神经网络的方法。

One of the earliest approaches to entity alignment involves similarity-based methods. These methods determine whether two entities align by calculating their similarity. Techniques include string similarity, which compares features like character composition and word spelling [15], and graph similarity, which evaluates the similarity between neighboring nodes within the entities’ respective subgraphs [16].
实体对齐的最早方法之一是基于相似度的方法。这些方法通过计算两个实体的相似度来判断它们是否对齐。技术包括字符串相似度，比较字符组成和单词拼写等特征[15]，以及图相似度，评估实体各自子图中邻近节点之间的相似性[16]。

Scharffe et al. [17] developed the RDF-AI entity alignment framework, comprising five modules: preprocessing, matching, fusion, linking, and post-processing. Notably, the matching module utilizes a fuzzy string matching algorithm [18] that significantly enhances the efficiency of string similarity comparisons. Pershina et al. [16] introduced the HolisticEM model for entity alignment. Initially, a graph of potentially matching entity pairs was constructed by assessing word correlations using Inverse Document Frequency (IDF) [19]. The model then facilitated entity alignment in large-scale knowledge graphs through the calculation of graph similarity, employing a personalized webpage ranking algorithm. However, similarity-based entity alignment methods exhibit several weaknesses. Primarily, these approaches depend on predefined rules and similarity metrics, which hinder their ability to effectively handle the intricate diversity of entity representations within the domain of aeronautical metrology. Additionally, they are
Scharffe 等人[17]开发了 RDF-AI 实体对齐框架，该框架包含五个模块：预处理、匹配、融合、链接和后处理。值得注意的是，匹配模块采用了一种模糊字符串匹配算法[18]，显著提升了字符串相似度比较的效率。Pershina 等人[16]提出了 HolisticEM 实体对齐模型。最初，通过使用逆文档频率（IDF）[19]评估词语相关性，构建了潜在匹配实体对的图。该模型随后通过计算图相似度，利用个性化网页排名算法，实现了大规模知识图谱中的实体对齐。然而，基于相似度的实体对齐方法存在若干不足。首先，这些方法依赖预定义规则和相似度度量，限制了其有效处理航空计量领域内实体表示复杂多样性的能力。此外，它们还存在...
particularly susceptible to noise and lack robustness, which becomes evident when aligning metrological equipment entities with variant nomenclatures. Consequently, these limitations render similarity-based methods less effective for knowledge fusion tasks in aeronautical metrology.
特别容易受到噪声影响且缺乏鲁棒性，这在对具有不同命名的计量设备实体进行对齐时尤为明显。因此，这些限制使得基于相似度的方法在航空计量的知识融合任务中效果较差。

The knowledge graph embedding-based method involves embedding entities and relations into a continuous vector space, where entities with similar characteristics are positioned closely. This method computes the vector representation of entities and relations to determine their similarity, facilitating entity alignment. The TransE model [20] represents a seminal approach to representation learning for translations and marks a significant milestone in knowledge graph embedding research. Its core concept revolves around treating relationships as vector transformations within the same vector space, mapping head entities to tail entities.
基于知识图谱嵌入的方法涉及将实体和关系嵌入到连续的向量空间中，其中具有相似特征的实体被定位得较近。该方法通过计算实体和关系的向量表示来确定它们的相似度，从而实现实体对齐。TransE 模型[20]是翻译表示学习的开创性方法，也是知识图谱嵌入研究的重要里程碑。其核心思想是将关系视为同一向量空间内的向量变换，将头实体映射到尾实体。

Translation-based representation learning offers advantages, including a small number of parameters and concise representations. Consequently, numerous entity alignment models employing knowledge graph embeddings have been developed. For instance, the RotatE model [21] conceptualizes each relationship as a rotation from the source entity to the target entity within a complex vector space, thereby enhancing the model’s capacity to capture inter-entity relationships. The HAKE model [22] situates entities within a polar coordinate system to effectively depict their semantic hierarchies. The ConvE model [23] employs multilayer convolution to elucidate the semantic relationships between entity pairs, facilitating efficient entity alignment. In addition to the previously discussed translation-based methods, semantic matching approaches also play a crucial role in the realm of knowledge graph representation learning. The MtransE model [24] employs the TransE algorithm to learn embeddings for entities in multiple languages, facilitating cross-lingual entity alignment. The BootEA model [25] enhances alignment model performance through the integration of a bootstrapping strategy and self-supervised learning. Additionally, the TransEdge model [26] addresses the challenge of entity matching across graph edges by incorporating unique edge embedding vectors. Zhu et al. [27] summarized the graph embedding-based entity alignment approach, introduced a new EA framework with modules for information aggregation, entity alignment, and post-alignment, and validated its effectiveness through experiments. Tian et al. [28] proposed the ExEA framework to generate explanations for interpreting and correcting embedding-based EA results. This method constructs matching subgraphs and alignment dependency graphs to explain and resolve conflicts in entity alignment. Guo et al. [29] proposed a method for entity alignment in the civil aviation domain using translation embeddings. This method separately embeds the semantic descriptions, relations, and attributes of entities, offering advantages for entity alignment tasks within this domain. Wang et al. [30] introduced an entity alignment method based on a Siamese network and multi-attribute importance features. By incorporating a font pre-training model and a character feature layer with a multi-attribute attention mechanism, this method enhances the completeness and reliability of the civil aviation knowledge graph. However, the above models struggle to effectively represent many-to-many metrological traceability relationships in their generation of entity relationship vectors. Furthermore, these models face challenges in fully capturing the semantic information of multi-attribute aeronautical metrology entities, thereby constraining their performance.
基于翻译的表示学习具有参数少、表示简洁等优势。因此，许多采用知识图谱嵌入的实体对齐模型被提出。例如，RotatE 模型[21]将每个关系概念化为从源实体到目标实体在复数向量空间中的旋转，从而增强了模型捕捉实体间关系的能力。HAKE 模型[22]将实体置于极坐标系中，有效地描绘了它们的语义层次结构。ConvE 模型[23]采用多层卷积来阐释实体对之间的语义关系，促进了高效的实体对齐。除了上述基于翻译的方法，语义匹配方法在知识图谱表示学习领域也起着关键作用。MtransE 模型[24]利用 TransE 算法学习多语言实体的嵌入，促进跨语言实体对齐。 BootEA 模型[25]通过引入自举策略和自监督学习提升了对齐模型的性能。此外，TransEdge 模型[26]通过引入独特的边嵌入向量，解决了跨图边的实体匹配问题。Zhu 等人[27]总结了基于图嵌入的实体对齐方法，提出了包含信息聚合、实体对齐和后对齐模块的新型 EA 框架，并通过实验验证了其有效性。Tian 等人[28]提出了 ExEA 框架，用于生成解释以解读和纠正基于嵌入的实体对齐结果。该方法构建匹配子图和对齐依赖图，以解释和解决实体对齐中的冲突。Guo 等人[29]提出了一种基于翻译嵌入的民航领域实体对齐方法，该方法分别嵌入实体的语义描述、关系和属性，针对该领域的实体对齐任务具有优势。Wang 等人[30]引入了一种基于孪生网络和多属性重要性特征的实体对齐方法。 通过引入字体预训练模型和带有多属性注意力机制的字符特征层，该方法增强了民航知识图谱的完整性和可靠性。然而，上述模型在生成实体关系向量时难以有效表示多对多的计量溯源关系。此外，这些模型在充分捕捉多属性航空计量实体的语义信息方面存在挑战，从而限制了其性能。

Graph neural network (GNN) approaches leverage graph models to represent entities and their relationships within a knowledge graph. By aggregating neighboring entities, these methods enhance entity embeddings, allowing them to effectively capture both local and global
图神经网络（GNN）方法利用图模型来表示知识图谱中的实体及其关系。通过聚合邻近实体，这些方法增强了实体嵌入，使其能够有效捕捉局部和全局
structural node information. Consequently, GNNs can more accurately identify similar entities across different knowledge graphs.
结构节点信息。因此，GNN 能够更准确地识别不同知识图谱中的相似实体。

The GCN-Align model [31], an early entity alignment model, leverages graph convolutional networks to embed entities from diverse languages into a unified vector space. It integrates structural and attribute embeddings to facilitate cross-language entity alignment. The NAEA model [32] uses a neighborhood attention mechanism to assign varying attention weights to entity neighbors, thereby learning entity representations through the aggregation of neighborhood information. Chen et al. [33] proposed a high-order graph neural network HOLI-GNN for knowledge graph entity alignment. This model addresses the issue of excessive smoothing from neighborhood aggregation by introducing a local inflation mechanism. Song et al. [34] developed a weakly supervised group mask network (WSGMN), which enhances target object recognition by integrating contextual information through community instance generation. Recently, unsupervised and self-supervised methods have been introduced to reduce reliance on labeled data. Zeng et al. [35] proposed MultiEM, an unsupervised approach for multitable entity matching. This model improves matching efficiency and effectiveness through enhanced entity representation, hierarchical merging, and density-based pruning. Ge et al. [36] introduced a selfsupervised entity matching framework, CollaborEM, which performs entity matching without manual labeling by leveraging multi-feature collaboration. This framework effectively identifies tuple features in a fault-tolerant manner, generating reliable matching results. Additionally, methods to optimize entity embeddings and neighborhood aggregation are proposed to enhance entity alignment performance further. The GRGCN model [37] integrates entity structure, attributes, and attention mechanisms via multilevel learning, assigning varied weights to each node’s neighbors to enhance spatial information capture. The AliNet model [38] employs a gating mechanism to assimilate multi-hop neighborhood information of entities, simultaneously diminishing noise from distant neighbors using an attention mechanism. The DvGNet model [39] addresses both entity and relational interactions, reducing the impact of structural heterogeneity on entity alignment. Given the notable benefits of such methods in enriching entity neighbor information, this study employs GNN to facilitate the structural embedding of nodes. Distinctively, this paper introduces a multi-scale node aggregation strategy designed to improve the aggregation of neighbor information for long-tailed entities.
GCN-Align 模型[31]是一种早期的实体对齐模型，利用图卷积网络将来自不同语言的实体嵌入到统一的向量空间中。它整合了结构和属性嵌入，以促进跨语言实体对齐。NAEA 模型[32]采用邻域注意力机制，为实体邻居分配不同的注意力权重，从而通过聚合邻域信息学习实体表示。Chen 等人[33]提出了一种高阶图神经网络 HOLI-GNN 用于知识图谱实体对齐。该模型通过引入局部膨胀机制，解决了邻域聚合导致的过度平滑问题。Song 等人[34]开发了一种弱监督群组掩码网络（WSGMN），通过社区实例生成整合上下文信息，增强目标对象识别能力。近年来，出现了无监督和自监督方法，以减少对标注数据的依赖。Zeng 等人[35]提出了 MultiEM，一种用于多表实体匹配的无监督方法。 该模型通过增强实体表示、分层合并和基于密度的剪枝，提高了匹配的效率和效果。Ge 等人[36]提出了一个自监督实体匹配框架 CollaborEM，该框架通过多特征协作实现无人工标注的实体匹配。该框架以容错方式有效识别元组特征，生成可靠的匹配结果。此外，还提出了优化实体嵌入和邻域聚合的方法，以进一步提升实体对齐性能。GRGCN 模型[37]通过多层次学习整合实体结构、属性和注意力机制，为每个节点的邻居分配不同权重，以增强空间信息的捕获能力。AliNet 模型[38]采用门控机制融合实体的多跳邻域信息，同时利用注意力机制减少远邻的噪声影响。DvGNet 模型[39]同时处理实体和关系交互，降低结构异质性对实体对齐的影响。 鉴于此类方法在丰富实体邻居信息方面的显著优势，本研究采用 GNN 来促进节点的结构嵌入。本文独特地引入了一种多尺度节点聚合策略，旨在提升长尾实体邻居信息的聚合效果。

This section first introduces foundational concepts related to knowledge graphs and entity alignment. Subsequently, it details the general architecture and individual components of the proposed model.
本节首先介绍与知识图谱和实体对齐相关的基础概念。随后，详细说明所提模型的一般架构及各个组成部分。

The AMKG expresses the concepts and their relationships in the metrological traceability system in terms of several triples, which can be defined as $AMKG=(E,R,A,T^R,V)$$AMKG=\left(E,R,A,T^R,V\right)$AMKG=(E,R,A,T^(R),V)A M K G=\left(E, R, A, T^{R}, V\right). where $E,R,A$$E,R,A$E,R,AE, R, A denotes the set of entities, relationships, and attributes, respectively, $T^R$$T^R$T^(R)T^{R} denotes the relationship ternary, and $V$$V$VV denotes the attribute value of an entity. Each ternary $t_k=(e_i,r_{ij},e_j)$$t_k=\left(e_i,r_{ij},e_j\right)$t_(k)=(e_(i),r_(ij),e_(j))t_{k}=\left(e_{i}, r_{i j}, e_{j}\right) denotes the relationship between the head entity $e_i$$e_i$e_(i)e_{i} for the tail entity $e_j$$e_j$e_(j)e_{j} as $r_{ij}$$r_{ij}$r_(ij)r_{i j}, where $t\in T,e\in E,r\in R$$t\in T,e\in E,r\in R$t in T,e in E,r in Rt \in T, e \in E, r \in R.
AMKG 以多个三元组的形式表达计量溯源系统中的概念及其关系，这些三元组可以定义为 $AMKG=(E,R,A,T^R,V)$$AMKG=\left(E,R,A,T^R,V\right)$AMKG=(E,R,A,T^(R),V)A M K G=\left(E, R, A, T^{R}, V\right) ，其中 $E,R,A$$E,R,A$E,R,AE, R, A 分别表示实体、关系和属性的集合， $T^R$$T^R$T^(R)T^{R} 表示关系三元组， $V$$V$VV 表示实体的属性值。每个三元组 $t_k=(e_i,r_{ij},e_j)$$t_k=\left(e_i,r_{ij},e_j\right)$t_(k)=(e_(i),r_(ij),e_(j))t_{k}=\left(e_{i}, r_{i j}, e_{j}\right) 表示头实体 $e_i$$e_i$e_(i)e_{i} 与尾实体 $e_j$$e_j$e_(j)e_{j} 之间的关系为 $r_{ij}$$r_{ij}$r_(ij)r_{i j} ，其中 $t\in T,e\in E,r\in R$$t\in T,e\in E,r\in R$t in T,e in E,r in Rt \in T, e \in E, r \in R 。

The goal of entity alignment is to find the set of remaining aligned entity pairs based on $AMK{G}_1=(E_1,R_1,A_1,T_1^R,V_1)$$AMK{G}_1=\left(E_1,R_1,A_1,T_1^R,V_1\right)$AMKG_(1)=(E_(1),R_(1),A_(1),T_(1)^(R),V_(1))A M K G_{1}=\left(E_{1}, R_{1}, A_{1}, T_{1}^{R}, V_{1}\right) and $AMK{G}_2=(E_2$$AMK{G}_2=\left(E_2\right.$AMKG_(2)=(E_(2):}A M K G_{2}=\left(E_{2}\right., $R_2,A_2,T_2^R,V_2$$R_2,A_2,T_2^R,V_2$R_(2),A_(2),T_(2)^(R),V_(2)R_{2}, A_{2}, T_{2}^{R}, V_{2} ), based on a given seed set of pre-aligned entity pair $t=$$t=$t=t= $(e_i^1,e_i^2)$$\left(e_i^1,e_i^2\right)$(e_(i)^(1),e_(i)^(2))\left(e_{i}^{1}, e_{i}^{2}\right) where $e_i^1\in AMK{G}_1,e_i^2\in AMK{G}_2$$e_i^1\in AMK{G}_1,e_i^2\in AMK{G}_2$e_(i)^(1)in AMKG_(1),e_(i)^(2)in AMKG_(2)e_{i}^{1} \in A M K G_{1}, e_{i}^{2} \in A M K G_{2}.
实体对齐的目标是在给定预先对齐实体对的种子集 $t=$$t=$t=t= $(e_i^1,e_i^2)$$\left(e_i^1,e_i^2\right)$(e_(i)^(1),e_(i)^(2))\left(e_{i}^{1}, e_{i}^{2}\right) ，基于 $AMK{G}_1=(E_1,R_1,A_1,T_1^R,V_1)$$AMK{G}_1=\left(E_1,R_1,A_1,T_1^R,V_1\right)$AMKG_(1)=(E_(1),R_(1),A_(1),T_(1)^(R),V_(1))A M K G_{1}=\left(E_{1}, R_{1}, A_{1}, T_{1}^{R}, V_{1}\right) 和 $AMK{G}_2=(E_2$$AMK{G}_2=\left(E_2\right.$AMKG_(2)=(E_(2):}A M K G_{2}=\left(E_{2}\right. ， $R_2,A_2,T_2^R,V_2$$R_2,A_2,T_2^R,V_2$R_(2),A_(2),T_(2)^(R),V_(2)R_{2}, A_{2}, T_{2}^{R}, V_{2} ，找到剩余对齐实体对的集合，其中 $e_i^1\in AMK{G}_1,e_i^2\in AMK{G}_2$$e_i^1\in AMK{G}_1,e_i^2\in AMK{G}_2$e_(i)^(1)in AMKG_(1),e_(i)^(2)in AMKG_(2)e_{i}^{1} \in A M K G_{1}, e_{i}^{2} \in A M K G_{2} 。

This paper introduces the Multi-perspective Embedding-based Entity Alignment (MEEA) model, designed to enhance the integrity of AMKG.
本文介绍了多视角嵌入实体对齐（MEEA）模型，旨在提升 AMKG 的完整性。

By removing ambiguous and redundant entities and integrating diverse aeronautical metrological knowledge from various sources, MEEA ensures the quality of the knowledge graph. Fig. 1 illustrates the model’s architecture, which comprises three main components: the input AMKGs, multi-perspective embedding, and entity alignment. Firstly, the inputs consist of two distinct AMKGs, denoted as $AMK{G}_1$$AMK{G}_1$AMKG_(1)A M K G_{1} and $AMK{G}_2$$AMK{G}_2$AMKG_(2)A M K G_{2}. In $AMK{G}_1$$AMK{G}_1$AMKG_(1)A M K G_{1}, semantic information regarding an entity $e_i^1$$e_i^1$e_(i)^(1)e_{i}^{1} is acquired from three perspectives: structure, relation, and attribute. The structure embedding involves employing a multi-scale GNN to amalgamate multihop neighbor information about $e_i^1$$e_i^1$e_(i)^(1)e_{i}^{1}. Notably, a gating mechanism is employed to amalgamate the hidden and output layers of the network, thereby yielding a more precise representation of the entity. The relation embedding is based on the TransD model [40]. The attribute embedding employs the BERT model to allocate attention weights to each attribute name and value of entity $e_i^1$$e_i^1$e_(i)^(1)e_{i}^{1}. The same method applies to entity $e_i^2$$e_i^2$e_(i)^(2)e_{i}^{2} in $AMK{G}_2$$AMK{G}_2$AMKG_(2)A M K G_{2}. For entity alignment, the alignment between entities $e_i^1$$e_i^1$e_(i)^(1)e_{i}^{1} and $e_i^2$$e_i^2$e_(i)^(2)e_{i}^{2} is determined by calculating the cosine distance between their final embedding vectors.
通过去除模糊和冗余实体，并整合来自多种来源的多样化航空气象知识，MEEA 确保了知识图谱的质量。图 1 展示了模型的架构，包含三个主要部分：输入的 AMKGs、多视角嵌入和实体对齐。首先，输入由两个不同的 AMKGs 组成，分别表示为 $AMK{G}_1$$AMK{G}_1$AMKG_(1)A M K G_{1} 和 $AMK{G}_2$$AMK{G}_2$AMKG_(2)A M K G_{2} 。在 $AMK{G}_1$$AMK{G}_1$AMKG_(1)A M K G_{1} 中，关于实体 $e_i^1$$e_i^1$e_(i)^(1)e_{i}^{1} 的语义信息从结构、关系和属性三个视角获取。结构嵌入采用多尺度 GNN 融合关于 $e_i^1$$e_i^1$e_(i)^(1)e_{i}^{1} 的多跳邻居信息。值得注意的是，采用门控机制融合网络的隐藏层和输出层，从而生成更精确的实体表示。关系嵌入基于 TransD 模型[40]。属性嵌入采用 BERT 模型为实体 $e_i^1$$e_i^1$e_(i)^(1)e_{i}^{1} 的每个属性名称和值分配注意力权重。相同方法适用于 $AMK{G}_2$$AMK{G}_2$AMKG_(2)A M K G_{2} 中的实体 $e_i^2$$e_i^2$e_(i)^(2)e_{i}^{2} 。对于实体对齐，通过计算实体 $e_i^1$$e_i^1$e_(i)^(1)e_{i}^{1} 和 $e_i^2$$e_i^2$e_(i)^(2)e_{i}^{2} 最终嵌入向量之间的余弦距离来确定它们的对齐关系。

The core idea of GNN is to aggregate information from neighboring nodes to update the representation of the central node. In the messagepassing phase, those entities with more neighboring nodes are called key nodes because they can aggregate a large amount of information. On the contrary, those entities that appear less frequently and have fewer neighboring nodes are called long-tail entities. Long-tail entities are prevalent in AMKGs. These entities typically include rare and specialized metrology equipment and specific metrology protocols, such as ultra-low-temperature gas flow standard devices and turbine flowmeter protocols. Despite their infrequent appearance in AMKGs, they are crucial for ensuring the performance quality of specific aerospace products.
GNN 的核心思想是从邻居节点聚合信息以更新中心节点的表示。在消息传递阶段，邻居节点较多的实体被称为关键节点，因为它们可以聚合大量信息。相反，出现频率较低且邻居节点较少的实体被称为长尾实体。长尾实体在 AMKG 中普遍存在。这些实体通常包括稀有且专业的计量设备和特定的计量协议，例如超低温气体流量标准装置和涡轮流量计协议。尽管它们在 AMKG 中出现频率较低，但对于确保特定航天产品的性能质量至关重要。

The limitations of traditional GNNs, such as graph convolutional networks (GCN) [41] and graph attention networks (GAT) [42], in handling long-tailed entities are significant. In a single-layer network, as shown in Fig. 2, entity e is connected to only one neighbor, d, resulting in limited information aggregation. While increasing the number of network layers can introduce additional neighbor information, it also leads to over-smoothing. After multiple layers of aggregation, the representations of long-tailed entities become similar to other entities, reducing their distinctiveness. To tackle this limitation, this paper introduces the MGCN model. The model adeptly integrates an attention mechanism, which assigns varied weights to each neighboring node according to their relative importance. This approach is particularly effective when addressing entities with a long-tail entity e. By employing an expanded convolution kernel, the model efficiently aggregates the pertinent features from two-hop neighbors, nodes c and f. During the iterative propagation process of MGCN, the rich information accumulated by long-tail entities can be disseminated to other entities, thereby enhancing the depth and breadth of AMKG information circulation. The target nodes are able to effectively learn the deep knowledge representation embedded in complex structures, which facilitates entity alignment in AMKG.
传统图神经网络（GNN），如图卷积网络（GCN）[41]和图注意力网络（GAT）[42]，在处理长尾实体时存在显著局限性。如图 2 所示，在单层网络中，实体 e 仅与一个邻居 d 相连，导致信息聚合有限。虽然增加网络层数可以引入更多邻居信息，但也会导致过度平滑。经过多层聚合后，长尾实体的表示变得与其他实体相似，降低了其区分度。为了解决这一限制，本文引入了 MGCN 模型。该模型巧妙地整合了注意力机制，根据邻居节点的相对重要性赋予不同权重。这种方法在处理长尾实体 e 时尤为有效。通过采用扩展卷积核，模型能够高效地聚合来自二跳邻居节点 c 和 f 的相关特征。 在 MGCN 的迭代传播过程中，长尾实体积累的丰富信息可以传播到其他实体，从而增强 AMKG 信息流通的深度和广度。目标节点能够有效学习嵌入复杂结构中的深层知识表示，这有助于 AMKG 中的实体对齐。

For an entity $e_i$$e_i$e_(i)e_{i} in KG, its embedding in layer $l$$l$ll can be computed as:
对于 KG 中的实体 $e_i$$e_i$e_(i)e_{i} ，其在第 $l$$l$ll 层的嵌入可以计算为：
$h_{e_i}^l=\sigma \left(\sum _{e_j\in N_{e_i}}\sum _{r_k\in R_{ij}}{\alpha }_{ijk}^{l-1}{W}_{r_k}{h}_{e_j}^{l-1}\right)$$h_{e_i}^l=\sigma \left(\sum _{e_j\in N_{e_i}} \sum _{r_k\in R_{ij}} {\alpha }_{ijk}^{l-1}{W}_{r_k}{h}_{e_j}^{l-1}\right)$h_(e_(i))^(l)=sigma(sum_(e_(j)inN_(e_(i)))sum_(r_(k)inR_(ij))alpha_(ijk)^(l-1)W_(r_(k))h_(e_(j))^(l-1))h_{e_{i}}^{l}=\sigma\left(\sum_{e_{j} \in N_{e_{i}}} \sum_{r_{k} \in R_{i j}} \alpha_{i j k}^{l-1} W_{r_{k}} h_{e_{j}}^{l-1}\right)
where $\sigma (\cdot )$$\sigma (\cdot )$sigma(*)\sigma(\cdot) is the activation function of $\mathrm{LeakyReLU}(\cdot ),N_{e_i}$$\mathrm{LeakyReLU}(\cdot ),N_{e_i}$LeakyReLU(*),N_(e_(i))\operatorname{LeakyReLU}(\cdot), N_{e_{i}} is the neighboring nodes of $e_i,R_{ij}$$e_i,R_{ij}$e_(i),R_(ij)e_{i}, R_{i j} is all the relations between $e_i$$e_i$e_(i)e_{i} and $e_j,r_k$$e_j,r_k$e_(j),r_(k)e_{j}, r_{k} is the $k$$k$kk th edge of $e_i$$e_i$e_(i)e_{i} and $e_j,W_{r_k}$$e_j,W_{r_k}$e_(j),W_(r_(k))e_{j}, W_{r_{k}} is an orthogonal matrix, which guarantees the norms and the relative distances of entities remain unchanged after transformation, and ${\alpha }_{ijk}^{l-1}$${\alpha }_{ijk}^{l-1}$alpha_(ijk)^(l-1)\alpha_{i j k}^{l-1} is the attention coefficient when aggregating
其中 $\sigma (\cdot )$$\sigma (\cdot )$sigma(*)\sigma(\cdot) 是激活函数， $\mathrm{LeakyReLU}(\cdot ),N_{e_i}$$\mathrm{LeakyReLU}(\cdot ),N_{e_i}$LeakyReLU(*),N_(e_(i))\operatorname{LeakyReLU}(\cdot), N_{e_{i}} 是 $e_i,R_{ij}$$e_i,R_{ij}$e_(i),R_(ij)e_{i}, R_{i j} 的邻居节点， $e_i$$e_i$e_(i)e_{i} 和 $e_j,r_k$$e_j,r_k$e_(j),r_(k)e_{j}, r_{k} 之间的所有关系是 $k$$k$kk ， $e_i$$e_i$e_(i)e_{i} 的第 $k$$k$kk 条边是 $e_j,W_{r_k}$$e_j,W_{r_k}$e_(j),W_(r_(k))e_{j}, W_{r_{k}} ， $e_j,W_{r_k}$$e_j,W_{r_k}$e_(j),W_(r_(k))e_{j}, W_{r_{k}} 是一个正交矩阵，保证变换后实体的范数和相对距离保持不变， ${\alpha }_{ijk}^{l-1}$${\alpha }_{ijk}^{l-1}$alpha_(ijk)^(l-1)\alpha_{i j k}^{l-1} 是在聚合时的注意力系数。

Fig. 1. Overview of MEEA model.
图 1. MEEA 模型概述。

Fig. 2. Multi-scale node aggregation process.
图 2. 多尺度节点聚合过程。
different neighboring nodes, calculated as:
不同邻居节点，计算公式为：
${\alpha }_{ijk}^{l-1}={\mathrm{Softmax}}_k\left(a^T(W_{r_k}{h}_{e_i}^{l-1}\oplus W_{r_k}{h}_{e_j}^{l-1}\oplus h_{r_k})\right)$${\alpha }_{ijk}^{l-1}={\mathrm{Softmax}}_k\left(a^T\left(W_{r_k}{h}_{e_i}^{l-1}\oplus W_{r_k}{h}_{e_j}^{l-1}\oplus h_{r_k}\right)\right)$alpha_(ijk)^(l-1)=Softmax_(k)(a^(T)(W_(r_(k))h_(e_(i))^(l-1)o+W_(r_(k))h_(e_(j))^(l-1)o+h_(r_(k))))\alpha_{i j k}^{l-1}=\operatorname{Softmax}_{k}\left(a^{T}\left(W_{r_{k}} h_{e_{i}}^{l-1} \oplus W_{r_{k}} h_{e_{j}}^{l-1} \oplus h_{r_{k}}\right)\right)
where Softmax ${}_k$${}_k$_(k)_{k} is the normalization of the $k$$k$kk th edge attention coefficients of $e_i$$e_i$e_(i)e_{i} and $e_j,\oplus$$e_j,\oplus$e_(j),o+e_{j}, \oplus denotes the vector concatenation, and $a^T$$a^T$a^(T)a^{T} is the parameter of the learnable attention weights.
其中 Softmax ${}_k$${}_k$_(k)_{k} 是对 $e_i$$e_i$e_(i)e_{i} 的第 $k$$k$kk 条边注意力系数的归一化， $e_j,\oplus$$e_j,\oplus$e_(j),o+e_{j}, \oplus 表示向量拼接， $a^T$$a^T$a^(T)a^{T} 是可学习注意力权重的参数。

If the long-tailed entity $e_i$$e_i$e_(i)e_{i} has only one neighbor $e_j$$e_j$e_(j)e_{j}, its embedding in layer $l$$l$ll can be computed as:
如果长尾实体 $e_i$$e_i$e_(i)e_{i} 只有一个邻居 $e_j$$e_j$e_(j)e_{j} ，则其在第 $l$$l$ll 层的嵌入可以计算为：
$h_{e_i}^l=\sigma \left(\mathrm{Average}(h_{e_i}^{Sg1}+h_{e_i}^{Sg2}+h_{e_i}^{Sg3})\right)$$h_{e_i}^l=\sigma \left(\mathrm{Average}\left(h_{e_i}^{Sg1}+h_{e_i}^{Sg2}+h_{e_i}^{Sg3}\right)\right)$h_(e_(i))^(l)=sigma(Average(h_(e_(i))^(Sg1)+h_(e_(i))^(Sg2)+h_(e_(i))^(Sg3)))h_{e_{i}}^{l}=\sigma\left(\operatorname{Average}\left(h_{e_{i}}^{S g 1}+h_{e_{i}}^{S g 2}+h_{e_{i}}^{S g 3}\right)\right)
where $h_{e_i}^{Sg1},h_{e_i}^{Sg2},h_{e_i}^{Sg3}$$h_{e_i}^{Sg1},h_{e_i}^{Sg2},h_{e_i}^{Sg3}$h_(e_(i))^(Sg1),h_(e_(i))^(Sg2),h_(e_(i))^(Sg3)h_{e_{i}}^{S g 1}, h_{e_{i}}^{S g 2}, h_{e_{i}}^{S g 3} is the embedding of Subgraph1, Subgraph2, and Subgraph3 in Fig. 2, respectively. The solid line indicates the relationship direction of entities and the dashed line indicates the direction of information aggregation between entities.
其中 $h_{e_i}^{Sg1},h_{e_i}^{Sg2},h_{e_i}^{Sg3}$$h_{e_i}^{Sg1},h_{e_i}^{Sg2},h_{e_i}^{Sg3}$h_(e_(i))^(Sg1),h_(e_(i))^(Sg2),h_(e_(i))^(Sg3)h_{e_{i}}^{S g 1}, h_{e_{i}}^{S g 2}, h_{e_{i}}^{S g 3} 分别是图 2 中子图 1、子图 2 和子图 3 的嵌入。实线表示实体之间的关系方向，虚线表示实体之间信息聚合的方向。

The Subgraph1 phase computes information about the direct neighbors $e_j$$e_j$e_(j)e_{j} of $e_i$$e_i$e_(i)e_{i}.
子图 1 阶段计算 $e_i$$e_i$e_(i)e_{i} 的直接邻居 $e_j$$e_j$e_(j)e_{j} 的信息。
$h_{e_i}^{Sg1}={\alpha }_{ijk}^{l-1}{W}_{r_k}{h}_{e_j}^{l-1}$$h_{e_i}^{Sg1}={\alpha }_{ijk}^{l-1}{W}_{r_k}{h}_{e_j}^{l-1}$h_(e_(i))^(Sg1)=alpha_(ijk)^(l-1)W_(r_(k))h_(e_(j))^(l-1)h_{e_{i}}^{S g 1}=\alpha_{i j k}^{l-1} W_{r_{k}} h_{e_{j}}^{l-1}

The Subgraph2 phase computes information about the indirect neighbors $e_m$$e_m$e_(m)e_{m} of $e_j$$e_j$e_(j)e_{j}, i.e., neighbors of neighbors. Here, the information of all other neighbors $e_m$$e_m$e_(m)e_{m} of $e_j$$e_j$e_(j)e_{j} is considered.
子图 2 阶段计算 $e_j$$e_j$e_(j)e_{j} 的间接邻居 $e_m$$e_m$e_(m)e_{m} 的信息，即邻居的邻居。这里考虑了 $e_j$$e_j$e_(j)e_{j} 的所有其他邻居 $e_m$$e_m$e_(m)e_{m} 的信息。
$h_{e_i}^{Sg2}=\sum _{e_m\in N_{e_j}}\sum _{r_o\in R_{jm}}{\alpha }_{jmo}^{l-1}{W}_{r_o}{h}_{e_m}^{l-1}$$h_{e_i}^{Sg2}=\sum _{e_m\in N_{e_j}} \sum _{r_o\in R_{jm}} {\alpha }_{jmo}^{l-1}{W}_{r_o}{h}_{e_m}^{l-1}$h_(e_(i))^(Sg2)=sum_(e_(m)inN_(e_(j)))sum_(r_(o)inR_(jm))alpha_(jmo)^(l-1)W_(r_(o))h_(e_(m))^(l-1)h_{e_{i}}^{S g 2}=\sum_{e_{m} \in N_{e_{j}}} \sum_{r_{o} \in R_{j m}} \alpha_{j m o}^{l-1} W_{r_{o}} h_{e_{m}}^{l-1}
where $R_{jm}$$R_{jm}$R_(jm)R_{j m} is all relations between $e_j$$e_j$e_(j)e_{j} and $e_m,r_o$$e_m,r_o$e_(m),r_(o)e_{m}, r_{o} is the $o$$o$oo th edge of $e_j$$e_j$e_(j)e_{j} and $e_m,W_{r_o}$$e_m,W_{r_o}$e_(m),W_(r_(o))e_{m}, W_{r_{o}} is the transformation matrix of $r_o$$r_o$r_(o)r_{o}.
其中 $R_{jm}$$R_{jm}$R_(jm)R_{j m} 是 $e_j$$e_j$e_(j)e_{j} 和 $e_m,r_o$$e_m,r_o$e_(m),r_(o)e_{m}, r_{o} 之间的所有关系， $o$$o$oo 是 $e_j$$e_j$e_(j)e_{j} 的第 $o$$o$oo 条边， $e_m,W_{r_o}$$e_m,W_{r_o}$e_(m),W_(r_(o))e_{m}, W_{r_{o}} 是 $r_o$$r_o$r_(o)r_{o} 的变换矩阵。

The Subgraph3 phase computes the two-hop neighbor $e_n$$e_n$e_(n)e_{n} information of $e_i$$e_i$e_(i)e_{i}. Unlike Subgraph2, Subgraph3 focuses on computing information about all other neighbors of $e_j$$e_j$e_(j)e_{j} (except $e_i$$e_i$e_(i)e_{i} ).
Subgraph3 阶段计算 $e_i$$e_i$e_(i)e_{i} 的两跳邻居 $e_n$$e_n$e_(n)e_{n} 信息。与 Subgraph2 不同，Subgraph3 侧重于计算 $e_j$$e_j$e_(j)e_{j} 的所有其他邻居（除 $e_i$$e_i$e_(i)e_{i} 外）的信息。
$h_{e_i}^{Sg3}=\sum _{e_n\in (N_{e_j}-e_i)}\sum _{r_p\in (R_{jm}-R_{ij})}{\alpha }_{jmp}^{l-1}{W}_{r_p}{h}_{e_n}^{l-1}$$h_{e_i}^{Sg3}=\sum _{e_n\in \left(N_{e_j}-e_i\right)} \sum _{r_p\in \left(R_{jm}-R_{ij}\right)} {\alpha }_{jmp}^{l-1}{W}_{r_p}{h}_{e_n}^{l-1}$h_(e_(i))^(Sg3)=sum_(e_(n)in(N_(e_(j))-e_(i)))sum_(r_(p)in(R_(jm)-R_(ij)))alpha_(jmp)^(l-1)W_(r_(p))h_(e_(n))^(l-1)h_{e_{i}}^{S g 3}=\sum_{e_{n} \in\left(N_{e_{j}}-e_{i}\right)} \sum_{r_{p} \in\left(R_{j m}-R_{i j}\right)} \alpha_{j m p}^{l-1} W_{r_{p}} h_{e_{n}}^{l-1}
Therefore, MGCN not only accounts for direct neighbor relationships but also enhances entity representation through multi-hop information transfer, crucial for addressing long-tailed entities in knowledge graphs.
因此，MGCN 不仅考虑直接邻居关系，还通过多跳信息传递增强实体表示，这对于解决知识图谱中的长尾实体问题至关重要。

GNNs can capture multi-hop neighbor information through multilayer aggregation. However, this may also introduce more noise since not all neighbor information is beneficial to the model’s performance. For this reason, this paper introduces a gating mechanism to regulate the information flow and weight assignment. This mechanism can effectively reduce the effect of noise while capturing multi-hop neighbor information, thus improving the accuracy of entity representation. The details of the gating mechanism are shown in Fig. 3, where $\odot$$\odot$o.\odot represents Hadamard Product, and + represents matrix addition.
GNN 可以通过多层聚合捕获多跳邻居信息。然而，这也可能引入更多噪声，因为并非所有邻居信息都有利于模型性能。基于此，本文引入门控机制来调节信息流和权重分配。该机制能够在捕获多跳邻居信息的同时有效减少噪声影响，从而提升实体表示的准确性。门控机制的细节如图 3 所示，其中 $\odot$$\odot$o.\odot 表示 Hadamard 积，+表示矩阵加法。

Assuming the number of network layers $l=2$$l=2$l=2l=2, the embedding of entity $e_i$$e_i$e_(i)e_{i} under the gating mechanism can be computed by the following equation:
假设网络层数为 $l=2$$l=2$l=2l=2 ，在门控机制下实体 $e_i$$e_i$e_(i)e_{i} 的嵌入可以通过以下公式计算：
$h_{e_i}=g\cdot h_{e_i}^1+(1-g)\cdot h_{e_i}^2$$h_{e_i}=g\cdot h_{e_i}^1+(1-g)\cdot h_{e_i}^2$h_(e_(i))=g*h_(e_(i))^(1)+(1-g)*h_(e_(i))^(2)h_{e_{i}}=g \cdot h_{e_{i}}^{1}+(1-g) \cdot h_{e_{i}}^{2}
where $g$$g$gg is learnable weight parameter used as a gate to control the combination of the hidden layer and the output layer, and $h_{e_i,t}^1$$h_{e_i,t}^1$h_(e_(i),t)^(1)h_{e_{i}, t}^{1} and $h_{e_i,t}^2$$h_{e_i,t}^2$h_(e_(i),t)^(2)h_{e_{i}, t}^{2} are the hidden and output layer representations of the network, respectively.
其中 $g$$g$gg 是可学习的权重参数，用作门控以控制隐藏层和输出层的组合， $h_{e_i,t}^1$$h_{e_i,t}^1$h_(e_(i),t)^(1)h_{e_{i}, t}^{1} 和 $h_{e_i,t}^2$$h_{e_i,t}^2$h_(e_(i),t)^(2)h_{e_{i}, t}^{2} 分别是网络的隐藏层和输出层表示。

Here, when it is necessary to aggregate $k$$k$kk-hop ( $k>2$$k>2$k > 2k>2 ) neighbor information, it can be aggregated through a $k$$k$kk-layer network. Let ${\rho }_1(h_{e_i}^1,h_{e_i}^2)$${\rho }_1\left(h_{e_i}^1,h_{e_i}^2\right)$rho_(1)(h_(e_(i))^(1),h_(e_(i))^(2))\rho_{1}\left(h_{e_{i}}^{1}, h_{e_{i}}^{2}\right) be a gated combination of one-hop and two-hop neighbor aggregation, which can be found recursively by the following equation:
这里，当需要聚合 $k$$k$kk 跳（ $k>2$$k>2$k > 2k>2 ）邻居信息时，可以通过一个 $k$$k$kk 层网络进行聚合。令 ${\rho }_1(h_{e_i}^1,h_{e_i}^2)$${\rho }_1\left(h_{e_i}^1,h_{e_i}^2\right)$rho_(1)(h_(e_(i))^(1),h_(e_(i))^(2))\rho_{1}\left(h_{e_{i}}^{1}, h_{e_{i}}^{2}\right) 为一跳和两跳邻居聚合的门控组合，其递归计算公式如下：
$h_{e_i}={\rho }_{k-1}(\dots {\rho }_2({\rho }_1(h_{e_i}^1,h_{e_i}^2),h_{e_i}^3)\dots )$$h_{e_i}={\rho }_{k-1}\left(\dots {\rho }_2\left({\rho }_1\left(h_{e_i}^1,h_{e_i}^2\right),h_{e_i}^3\right)\dots \right)$h_(e_(i))=rho_(k-1)(dotsrho_(2)(rho_(1)(h_(e_(i))^(1),h_(e_(i))^(2)),h_(e_(i))^(3))dots)h_{e_{i}}=\rho_{k-1}\left(\ldots \rho_{2}\left(\rho_{1}\left(h_{e_{i}}^{1}, h_{e_{i}}^{2}\right), h_{e_{i}}^{3}\right) \ldots\right)
Therefore, the structural embedding loss of the entity can be calculated by the following equation:
因此，实体的结构嵌入损失可以通过以下公式计算：
${\mathcal{L}}_{str}=\sum _{(e_i,e_j)\in A^{+}}\sum _{(e_i^{\prime },e_j^{\prime })\in A-}max({\lambda }_{str}+\Vert h_{e_i}-h_{e_j}\Vert -\Vert h_{e_i^{\prime }}-h_{e_j^{\prime }}\Vert ,0)$${\mathcal{L}}_{str}=\sum _{\left(e_i,e_j\right)\in A^{+}} \sum _{\left(e_i^{\prime },e_j^{\prime }\right)\in A-} max\left({\lambda }_{str}+\left(h_{e_i}-h_{e_j}\right)-\left(h_{e_i^{\prime }}-h_{e_j^{\prime }}\right),0\right)$L_(str)=sum_((e_(i),e_(j))inA^(+))sum_((e_(i)^('),e_(j)^('))in A-)max(lambda_(str)+||h_(e_(i))-h_(e_(j))||-||h_(e_(i)^('))-h_(e_(j)^('))||,0)\mathscr{L}_{s t r}=\sum_{\left(e_{i}, e_{j}\right) \in A^{+}} \sum_{\left(e_{i}^{\prime}, e_{j}^{\prime}\right) \in A-} \max \left(\lambda_{s t r}+\left\|h_{e_{i}}-h_{e_{j}}\right\|-\left\|h_{e_{i}^{\prime}}-h_{e_{j}^{\prime}}\right\|, 0\right)
where $A^{+}$$A^{+}$A^(+)A^{+}and $A^{-}$$A^{-}$A^(-)A^{-}are the set of positive and negative samples for entity alignment, ${\lambda }_{str}$${\lambda }_{str}$lambda_(str)\lambda_{s t r} is the margin hyper-parameter separating entity alignment structure loss, and $\Vert \cdot \Vert$$\Vert \cdot \Vert$||*||\|\cdot\| denotes the $L_2$$L_2$L_(2)L_{2} vector paradigm.
其中 $A^{+}$$A^{+}$A^(+)A^{+} 和 $A^{-}$$A^{-}$A^(-)A^{-} 分别是实体对齐的正样本和负样本集合， ${\lambda }_{str}$${\lambda }_{str}$lambda_(str)\lambda_{s t r} 是区分实体对齐结构损失的边距超参数， $\Vert \cdot \Vert$$\Vert \cdot \Vert$||*||\|\cdot\| 表示 $L_2$$L_2$L_(2)L_{2} 向量范式。