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On entity alignment at scale

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Abstract

Knowledge graph (KG), as an effective approach of organizing and storing data, has received growing attention over the last decade. A KG can hardly reach completeness since there are always a large amount of new data emerging. To increase the scale and coverage of KGs, a possible solution is to incorporate data from other KGs, and entity alignment (EA) plays a vital role during this process. EA is the task of detecting the entities that refer to the same real-world object but come from different KGs. Although a pile of approaches have been put forward to tackle this task, they are mostly evaluated on datasets in small size and cannot deal with large-scale data in practice. In this work, we study the task of EA at scale and put forward a novel solution that can manage large-scale KG pairs and meanwhile achieve promising alignment performance. First, we devise seed-oriented graph partition strategies to divide large-scale KG pairs into smaller subgraph pairs. Next, within each subgraph pair, we learn the unified entity representations using existing methods and conceive a novel reciprocal alignment inference strategy to model the bi-directional alignment interactions, which can lead to more accurate alignment results. To further improve the scalability of reciprocal alignment inference, we put forward two variant strategies that can significantly reduce the memory and time costs at the expense of a small drop of effectiveness. Our proposal is generic and can be applied to existing representation learning-based EA models to improve their capability of dealing with large-scale KG pairs. Finally, we build a new EA dataset with millions of entities and conduct detailed experiments to validate that our proposed model can effectively cope with EA at scale. We also evaluate our proposed model against state-of-the-art baselines on popular EA datasets, and the extensive experiments demonstrate its effectiveness and superiority.

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Notes

  1. Note that the incorporation of additional information does not modify the nature of EA problem. Thus, to concentrate on the major challenges while keeping the problem simple, we focus on using only the structural information for EA.

  2. In the rest of the paper, we may use “distance” and “similarity” with obvious adaptation.

  3. Currently, in the mainstream EA benchmarks [14, 41], the number of source entities is equal to that of target entities, and the ground truth mappings conform to the 1-to-1 constraint. Nevertheless, in more general scenarios, these conditions do not necessarily hold [63].

  4. Notice that LIME is agnostic to the choice of structural learning models.

  5. The similarity measure sim is usually chosen from cosine similarity [41,42,43], Euclidean distance [8, 56, 64], or Manhattan distance [50,51,52].

  6. For tied elements, we follow the common practice and denote their ranks as the average of the ranks that would have been assigned to them.

  7. https://www.dbpedia.org/blog/dbpedia-is-now-interlinked-with-freebase-links-to-opencyc-updated/.

  8. Note that we do not compare with I-SBP, since it selects confident EA pairs to augment training data, which improves both the partition and the representation learning process. It corresponds to the semi-supervised setting in previous EA works [29, 43], which is usually not compared with the methods without the semi-supervised setting (e.g., LIME in this work) for fairness.

  9. We omit the efficiency comparison of methods using additional information since the processing of additional information is complicated and it is difficult to provide a fair assessment.

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Acknowledgements

This work was partially supported by NSFC under Grants Nos. 61872446 and 71971212 and NSF of Hunan Province under Grant No. 2019JJ20024.

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Authors and Affiliations

  1. Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, 410072, Hunan, China

    Weixin Zeng, Xiang Zhao, Xinyi Li & Jiuyang Tang

  2. Hong Kong University of Science and Technology (Guangzhou), Guangzhou, 511453, Guangdong, China

    Wei Wang

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  1. Weixin Zeng
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Appendices

Appendix

Correctness analysis

We discuss the performance of reciprocal alignment inference and the direct inference (baseline model) under different circumstances, as mentioned in Sect. 4.4.

Case 1 For the ground-truth entity pair (u, v):

$$\begin{aligned} \begin{aligned} u&= \mathop {\arg \max }\{sim({\varvec{v}},{\varvec{u}}^\prime ), u^\prime \in {\mathcal {E}}_s\}; \\ v&= \mathop {\arg \max }\{sim({\varvec{u}},{\varvec{v}}^\prime ), v^\prime \in {\mathcal {E}}_t\}, \end{aligned} \end{aligned}$$

We have already discussed this situation in Sect. 4.4, where the accurate similarity signal is provided by the representation learning process. In this case, both reciprocal alignment inference and direct alignment inference can generate the correct answer.

Case 2 For the ground-truth entity pair (u, v):

$$\begin{aligned} \begin{aligned} u&= \mathop {\arg \max }\{sim({\varvec{v}},{\varvec{u}}^\prime ), u^\prime \in {\mathcal {E}}_s\}; \\ v^*&= \mathop {\arg \max }\{sim({\varvec{u}},{\varvec{v}}^\prime ), v^\prime \in {\mathcal {E}}_t\}, \quad v^*\ne v, \end{aligned} \end{aligned}$$

In this case, the direct alignment inference cannot generate the correct answer, since it only considers u’s preference and would generate \((u,v^*)\) as the answer. In comparison, reciprocal alignment inference does not necessarily generate the correct answer. This is because we only know \(p_{u,v} = 1, p_{v,u} < 1\). Given any target entity \(v^\prime \), we can derive \(p_{u,v^\prime } \le 1, p_{v^\prime ,u} \le 1\). Thus, \(r_{u,v}\le r_{u,v^\prime }\), while we cannot compare \(r_{v,u}\) and \(r_{v^\prime ,u}\). Therefore, we also cannot compare \(p_{u\leftrightarrow v} = (r_{u,v} + r_{v,u})/2\) with \(p_{u\leftrightarrow v^\prime } = (r_{u,v^\prime } + r_{v^\prime ,u})/2\) as the exact values are unknown.

Case 3 For the ground-truth entity pair (u, v):

$$\begin{aligned} \begin{aligned} u^*&= \mathop {\arg \max }\{sim({\varvec{v}},{\varvec{u}}^\prime ), u^\prime \in {\mathcal {E}}_s\}, \quad u^*\ne u; \\ v&= \mathop {\arg \max }\{sim({\varvec{u}},{\varvec{v}}^\prime ), v^\prime \in {\mathcal {E}}_t\}, \end{aligned} \end{aligned}$$

In this case, the direct alignment inference can generate the correct answer since it only considers u’s preference. In comparison, reciprocal alignment inference does not necessarily generate the correct answer. This is because we only know \(p_{u,v} <1, p_{v,u} = 1\). Given any target entity \(v^\prime \), we can derive \(p_{u,v^\prime } \le 1, p_{v^\prime ,u} < 1\). Thus, \(r_{v,u}<r_{v^\prime ,u}\), while we cannot compare \(r_{u,v}\) and \(r_{u,v^\prime }\). Therefore, we also cannot compare \(p_{u\leftrightarrow v} = (r_{u,v} + r_{v,u})/2\) with \(p_{u\leftrightarrow v^\prime } = (r_{u,v^\prime } + r_{v^\prime ,u})/2\) as the exact values are unknown.

Case 4 For the ground-truth entity pair (u, v):

$$\begin{aligned} \begin{aligned} u^*&= \mathop {\arg \max }\{sim({\varvec{v}},{\varvec{u}}^\prime ), u^\prime \in {\mathcal {E}}_s\}, \quad u^*\ne u; \\ v^*&= \mathop {\arg \max }\{sim({\varvec{u}},{\varvec{v}}^\prime ), v^\prime \in {\mathcal {E}}_t\}, \quad v^*\ne v, \end{aligned} \end{aligned}$$

In this case, the direct alignment inference cannot generate the correct answer, since it only considers u’s preference and would generate \((u,v^*)\) as the answer. In comparison, reciprocal alignment inference does not necessarily generate the correct answer. This is because we only know \(p_{u,v}<1, p_{v,u} < 1\). Given any target entity \(v^\prime \), we can derive \(p_{u,v^\prime } \le 1, p_{v^\prime ,u} \le 1\). However, we cannot compare \(r_{v,u}\) and \(r_{v^\prime ,u}\), or \(r_{u,v}\) and \(r_{u,v^\prime }\). Therefore, we cannot compare \(p_{u\leftrightarrow v} = (r_{u,v} + r_{v,u})/2\) with \(p_{u\leftrightarrow v^\prime } = (r_{u,v^\prime } + r_{v^\prime ,u})/2\) as the exact values are unknown.

In all, the direct alignment inference strategy can only generate the correct results under Case 1 and Case 3, while our proposed reciprocal inference strategy can generate the correct results under Case 1, and have the chances of producing correct answers in the rest of the cases. Considering that the input similarity matrix is usually of relatively low accuracy (since the representation learning models cannot fully capture the relatedness among entities), our proposal tends to attain better results than direct alignment inference, which is empirically validated in the experiment.

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Zeng, W., Zhao, X., Li, X. et al. On entity alignment at scale. The VLDB Journal 31, 1009–1033 (2022). https://doi.org/10.1007/s00778-021-00703-3

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