Collective Entity Alignment for Knowledge Fusion of Power Grid Dispatching Knowledge Graphs

Linyao Yang, Chen Lv, Xiao Wang,, Ji Qiao, Weiping Ding,,Jun Zhang,, and Fei-Yue Wang,

Abstract—Knowledge graphs (KGs) have been widely accepted as powerful tools for modeling the complex relationships between concepts and developing knowledge-based services. In recent years, researchers in the field of power systems have explored KGs to develop intelligent dispatching systems for increasingly large power grids. With multiple power grid dispatching knowledge graphs (PDKGs) constructed by different agencies, the knowledge fusion of different PDKGs is useful for providing more accurate decision supports. To achieve this, entity alignment that aims at connecting different KGs by identifying equivalent entities is a critical step. Existing entity alignment methods cannot integrate useful structural, attribute, and relational information while calculating entities’ similarities and are prone to making many-to-one alignments, thus can hardly achieve the best performance. To address these issues, this paper proposes a collective entity alignment model that integrates three kinds of available information and makes collective counterpart assignments. This model proposes a novel knowledge graph attention network(KGAT) to learn the embeddings of entities and relations explicitly and calculates entities’ similarities by adaptively incorporating the structural, attribute, and relational similarities. Then, we formulate the counterpart assignment task as an integer programming (IP) problem to obtain one-to-one alignments. We not only conduct experiments on a pair of PDKGs but also evaluate our model on three commonly used cross-lingual KGs. Experimental comparisons indicate that our model outperforms other methods and provides an effective tool for the knowledge fusion of PDKGs.

I. INTRODUCTION

WITH the rapid deployment of renewable energy and the increase of power electronic equipments, power grids have become increasingly huge, complex, and dynamic cyberphysical systems [1], [2]. Traditional dispatching methods that rely heavily on dispatchers’ experience have had difficulty in meeting stability, reliability, and high tolerance requirements.Therefore, there is a need of artificial intelligence and intelligent decision support systems for power grid dispatching.Various machine learning techniques have been applied on diverse problems faced by power systems, such as decisionmaking in dispatching and control [3], the security and privacy protection of power data [4], the automatic maintenance of power equipment [5], and the forecasting and optimization[6], [7] of power flow.

Despite the superior performance of machine learning techniques on given problems, their intransparency hinders their further applications to power systems as they can raise severe issues [8]. Knowledge graphs (KGs) represent entities as well as their relationships into structured triples [9], [10], which provide an effective tool for developing explainable knowledge-based decision support systems [11], [12]. Recently,researchers in the field of power systems have looked into the construction of various KGs, among which PDKGs provide a useful tool for intelligent power grid dispatching. For instance,Fanet al. [13] proposed constructing PDKGs by extracting entities and identifying the dispatching patterns from the dispatch data based on the BiLSTM-CRF model. Similarly, Daiet al. [14] constructed PDKGs based on the heterogeneous information networks technique using artificial data generated by simulations and proved that more effective and explainable dispatching schemes could be efficiently generated from their constructed PDKGs with a case study.

An illustration of the PDKG constructed by Daiet al. [14] is shown in Fig. 1, in which an entity represents a category of power grid status, and a relation denotes a dispatching action that adjusts the power gird from one state to another. With this PDKG, once an emergency event happens, the current state can be matched with an entity. Then, a dispatch path to the target state can be generated, which is easy to understand and explain. Besides, PDKGs can be generated from dispatch records and texts like scheduling rules, which provide an explainable human-machine collaborative dispatching approach.

Fig. 1. The schematic of the PDKG, in which entities represent different power grid states and relations represent dispatching actions.

Due to the distributed and hierarchical dispatching characteristics of power grids, multiple PDKGs regarding various scenarios can be constructed by different regional dispatch centers or from the data collected from different dispatchers,which are complementary in knowledge. In [15], the authors have proven the benefits of knowledge fusion based on entity alignment for knowledge reasoning. Therefore, the entity alignment of PDKGs is critical for the fusion of dispatching knowledge, which has not been studied yet. The problem of entity alignment for multilingual DBPedia KGs has been investigated for a long time. Recently, the rapid development of graph embedding [16] has promoted plenty of embeddingbased entity alignment methods [17]–[22] that align entities based on their low-dimensional embeddings. The most recent models are devoted to leveraging side information, including entities’ names, descriptions, and their attributes’ names, to promote the performance [23]–[25]. PDKGs are different from cross-lingual KGs as the entity names and attribute names of PDKGs do not have translational consistencies or much semantic meanings. By contrast, PDKGs have many numerical attributes, which means that PDKGs can be viewed as directed attributed multi-relational graphs. However, there is lack of an entity alignment method that can effectively integrate the explicit structural, attribute, and relational information for the knowledge fusion of PDKGs. Furthermore, existing entity alignment methods cannot efficiently tackle the oneto-one alignment problem for two large sets of entities; thus,they can not achieve excellent performance on large-scale KGs.

To remedy these issues, this paper proposes a collective entity alignment model based on integer programming with adaptive feature fusion (IPEA) for the knowledge fusion of PDKGs. Essentially, our idea is to make full use of the structural, attribute, and relational information while calculating entities’ similarities and collectively assign counterparts with a one-to-one alignment constraint. To effectively extract multi-relational structural information, we devise a novel KGAT model that explicitly learns the correlations between entities and relations with their embeddings. We employ the co-attention mechanism [26] to adaptively adjust the significance of the three kinds of information and calculate the synthesized similarity matrix. After that, we collectively align entities while considering the differences in their similarity scores by formulating this task as an IP problem.

In short, we summarize our key contributions as follows:

1) We are the first to propose the knowledge fusion of PDKGs based on entity alignment, and present an effective IPEA model to collectively align entities.

2) We design a novel KGAT model to learn the relatedness of entities and relations explicitly. We adopt and also improve the co-attention mechanism by integrating the structure,attribute, and relation vectors to calculate entities’ similarities.

3) We propose that more accurate and robust alignment results can be obtained by solving an IP problem with the oneto-one alignment constraint.

4) We evaluate the proposed IPEA on both PDKGs and cross-lingual KGs. Experimental results demonstrate IPEA’s superior performance and evaluate the effectiveness of each proposed module.

The remainder of this paper is divided into following sections. Section II reviews the related work of knowledge graph embedding and entity alignment. Section III provides the problem statement and the details of our model. Empirical evaluation is given in Section IV, before Section V presents our conclusions. In addition, the abbreviations used in this paper are listed in Table I.

KEY ABBREVIATIOTNASB ULSEE DI IN THIS ARTICLE

II. RELATED WORK

Knowledge graph embedding and entity alignment have achieved rapid development in recent years. In this section,we briefly review these two fields and analyze their shortcomings.

A. Knowledge Graph Embedding

Over the past decade, significant progress has been made in KG embedding research. The core idea of KG embedding is to learn low-dimensional vectors of entities and relations that preserve their semantic relations to simplify downstream knowledge calculations. Most existing KG embedding techniques can be categorized into translational distance models and semantic matching models [27].

Translational distance models learn KG embedding based on distance scoring functions. The typical translational distance model is TransE [28], which interprets a relation as the translation from its head entity to its tail entity, i.e., h +r ≈t is satisfied for a triple (h,r,t), where h, r , and t indicate the embeddings ofh,r, andt, respectively. Plenty of models have been motivated by TransE due to its simplicity and efficiency,such as TransR [29] and TransD [30]. TransR represents entities and relations into distinct spaces and learns translations to project entities to their corresponding relation space. TransD improves TransR by replacing the projection matrix with two vectors to reduce the parameter size and improve its generalization.

Semantic matching models leverage similarity-based scoring functions to learn representations of KGs. The RESCAL model [31] is a representative of semantic matching models that decomposes high-dimensional entities and relations into a third-order tensor based on tensor factorization. DistMult [32]models the relation-associated tensor to diagonal tensors to simplify RESCAL. ComplEx [33] extends the embedding space to the complex space to model asymmetric relations.SME [34] learns semantic matching scores based on neural networks and uses entities’ and relations’ embeddings as inputs to get matching scores in the hidden layer.

B. Entity Alignment

The earliest entity alignment approaches require intensive human participation to design hand-crafted features or utilize external sources based on crowdsourcing [35], which suffer from heavy human efforts and cannot scale to large-scale KGs. Due to their applicability and robustness, embeddingbased methods have been applied in most recent studies.These methods first learn embedding vectors to represent entities of different KGs and then align entities by calculating their vectors’ similarities. The earliest embedding-based entity alignment methods employ translational distance embedding models, especially the TransE model, to capture structural features. Most of them embed different KGs into separated vector spaces and learn translations to map different vector spaces. Recent models tend to utilize graph convolutional networks (GCNs) to learn structural embeddings, which have better abilities to capture both local and global proximities of entities and can represent multiple KGs into a unified vector space by sharing the weights of different GCNs. However, the vanilla GCNs cannot model relation information, making them ill-suited for PDKGs.

Existing embedding-based entity alignment methods can be grouped into two categories: methods that only use structural embeddings and methods that use multi-type information.Specifically, the first group consists of 1) MTransE [17],which utilizes TransE to learn structural embeddings; 2)IPTransE [18], which improves the TransE-based entity alignment models based on iterative training; 3) BootEA [36],which designs a bootstrapping strategy to enrich training samples and improve embeddings; 4) TransEdge [37], which contextualizes the representations of relations and learns entities’and relations’ embeddings in an edge-centric way; 5) KECG[20], which proposes a semi-supervised entity alignment model based on the graph attention network (GAT) and TransE to enhance entities’ embeddings with attentive weights to neighbors; 6) AliNet [38], which proposes a novel GCN to aggregate both direct and distant neighborhood information to mitigate the non-isomorphism of neighborhood structures; 7)NAEA [39], which proposes a neighborhood-aware attention mechanism to incorporate sub-graph information; 8) MRAEA[40], which directly models cross-lingual entities’ representations based on the attentive aggregation of their bi-directional corrected entities’ and relations’ meta semantics; and 9) RSN[22], which utilizes a recurrent neural network with residual learning to learn entities’ embeddings with long-term relational dependencies.

The second group includes 1) JAPE [23], which proposes a joint attribute-preserving embedding model; 2) GCN-Align[19], which firstly adopts GCN to learn entity embeddings from structural and attribute information, and combines them to align entities; 3) VR-GCN [41], which proposes a vectorized GCN to learn both entities’ and relations’ embeddings for KGs; 4) RDGCN [42], which proposes a dual-GCN to learn embeddings from both the KG and its dual relation KG; 5)HGCN [25], which jointly and iteratively learns embeddings of entities and relations; 6) GM-Align [43], which learns a graph-level matching vector from local matching to solve a graph matching problem; 7) RsimEA [24], which incorporates the structural similarity between relations to improve alignment performance; 8) GM-EHD-JEA [44], which introduces the topic entity graph to model entities’ contextual information and proposes a graph attention-based solution to encode entities’ similarities; 9) DAT [26], which fuses semantic and structural information based on a degree-aware coattention mechanism; and 10) CEA [45], which proposes a collective framework that formulates entity alignment as a classic stable matching problem, and solves it with the deferred acceptance algorithm (DAA).

As discussed, although much effort has been dedicated to entity alignment, the noted algorithms suffer from the following limitations and challenges. 1) The richness of KG data has not been fully exploited. In particular, explicit information including structural, attribute, and relational information has not been effectively integrated with a unified framework. 2)The alignment strategies of most previous works are simple,and makes them easy to obtain many-to-one alignments.Although a few studies utilized DAA to satisfy the one-to-one alignment constraint, their results are sub-optimal because they cannot model the difference in the similarity scores between different entity pairs. 3) The knowledge fusion of domain-specific KGs such as PDKGs has not been touched by current studies. Toward these issues, we propose a collective entity alignment model for PDKGs that embeds entities and relations based on their structural similarities using a KGAT model and obtains synthetic similarities through adaptive fusion of the structural, attribute, and relational information.In the end, it efficiently assigns counterparts with a one-to-one constraint by solving a 0–1 IP problem.

III. METHODOLOGY

In this section, we formulate the mathematical problem of entity alignment for PDKGs and provide the details of our model. The key parameters used in the following sections are listed in Table II.

TABLE II KEY PARAMETERS USED IN THIS PAPER

A. Problem Definition

There are two constraints that should be considered while making collective alignment decisions, including consistency and exclusiveness constraints [46]. Specifically, the consistency constraint indicates that equivalent entities’ features should be similar since they reflect the same real-world entity.The exclusiveness constraint requires that an entity in a PDKG can only be aligned to one entity in another PDKG due to their uniqueness in each PDKG.

To tackle the above constraints, we propose an effective and unified entity alignment model called IPEA, which measures entities’ similarities with the adaptive fusion of multi-type information and collectively assigns counterparts by solving an IP problem. Our proposed model is presented in Fig. 2 and contains three stages:

1) First, we forward the triples to a well designed KGAT model to represent PDKGs as low-dimensional vectors based on known alignment seeds. Based on the relational embeddings learned by the KGAT model, relation alignment is carried out and entities’ connected relation types are encoded as relation vectors to indicate their relational similarities.

2) Then, we fuse the structure, relation, and attribute vectors adaptively with a co-attention network to determine entities’ synchronized similarities.

3) Finally, we formulate the counterpart assignment problem as an IP problem to optimize the total similarity between all the predicted equivalent entity pairs with the one-to-one constraint. By solving this problem, robust alignment results are obtained and highly confident predictions are selected as the enrichment for pre-alignment seeds of the next iteration.

Next, we elaborate upon the modules of IPEA.

B. Feature Generation

Given a pair of PDKGs, we design a novel KG embedding model named KGAT to learn entities’ and relations’ structural embeddings. The representation learning mechanism of the KGAT model comes under the graph neural networks(GNNs) framework. The key idea of GNNs is to aggregate neighboring information to update the central node’s representation. The vanilla GNNs operate on undirected and isomorphic graphs, which cannot utilize the useful relation information of KGs. To overcome this problem, KGAT borrows the idea of TransE and attentively aggregates the representations of neighboring entities as well as the corresponding relations while updating the representations of the central entity. To explicitly model the correlations between entities and relations with their representations, the attention weight between a tail entity and the corresponding head entity in thel-th layer is computed by the self-attention mechanism shown in Fig. 3,which can be represented by the following equation:

Fig. 2. Overview of IPEA model. The proposed model contains three iterative steps: the structural embedding generation by KGAT, the feature fusion based on the co-attention mechanism, and the collective counterpart assignment based on IP.

Fig. 3. An illustration of KGAT’s attention mechanism. The central tail entity attentively aggregates its head entities’ and the relations’ embeddings to update its embedding.

The network architecture of KGAT is illustrated in Fig. 4.The input includes a composition of two PDKGs and their prior alignment seedsS. The output is the embeddings of entities and relations of both PDKGs. For the semi-supervised entity alignment task, KGAT is trained to minimize the distance between the equivalent entities’ representations while maximizing that between the inequivalent entity pairs by minimizing the following triplet margin loss:

Fig. 4. The overview framework of KGAT. The input is two PDKGs with pre-aligned entities. Circled nodes in the output are the embeddings of entities and relations of the two PDKGs.

We require the relation types of two PDKGs to be aligned one-to-one, which is a stable matching problem and can be solved by the DAA [48]. To improve the efficiency of relation alignment, we first align the relation pairs with the smallest L2distances for each other and then assign relation pairs for the remaining relation sets using DAA.

Existing methods mainly capture the semantic information of attribute names. For the PDKGs, there are multiple numerical attributes about the states of the power grid. For example,in the PDKGs proposed in [14], each entity has 116 attributes in which each attribute represents a monitoring indicator of the power grid. Therefore, in this work, we propose utilizing the numerical attributes to compare the similarity of entities’attributes. We denote the attribute vector as →nfor simplicity.

C. Adaptive Feature Fusion (AFF)

For the training of the co-attention model, the loss function is designed to maximize the known equivalent entity pairs’similarity scores

D. Collective Counterpart Assignment

After obtaining the similarity scores for each pair of entities based on adaptive feature fusion, we can build two similarity matrices, i.e., S1→2and S2→1, in both directions. The (i,j) element of S1→2is set to the similarity betweenG1’si-th entity andG2’ sj-th entity, while that of S2→1is set to the similarity betweenG2’ si-th entity andG1’sj-th entity.

Fig. 5. An example of entity alignment based on different strategies. (a) Input PDKGs; (b) Similarity matrix of all entity pairs to be aligned; (c)–(e) Alignment prediction results of different strategies, where the solid lines represent correct predictions, whereas the dashed lines are erroneous predictions.

Typically, the counterpart assignment task is viewed as a stable matching problem with the exclusiveness one-to-one constraint. Hence, a few methods adopt the DAA method to coordinate the alignment process and assign entity counterparts collectively. However, the decision-making paradigm based on DAA might not suffice for producing satisfying alignments since it only considers entities’ priorities to other entities while ignoring the differences of similarity scores between different entity pairs. Fig. 5 shows an example to illustrate the potential problems faced by independent decision-making and the DAA-based collective counterpart assignment [49]. Assuming that we need to assign counterparts for the target entitiesv1,v2,v3, andv4from the source entitiesu1,u2,u3, andu4based on the similarity matrix as shown in Fig. 5(b) (the ground truth is{(u1,v1),(u2,v2),(u3,v3),(u4,v4)}), the latter three entity pairs would be assigned incorrectly following the independent decision-making strategy,which only considers the similarity score between entities.However, if we only impose the one-to-one constraint while assigning counterparts, we will arrive at the results shown in Fig. 5(d), which is still not the best result because it ignores the similarity scores while encountering conflicts. To address this issue, we formulate the counterpart assignment task as an IP problem to deal with the consistency and exclusiveness constraints simultaneously.

wheresijis the (i,j) element of S, indicating the similarity score betweenG1’ si-th entity andG2’ sj-th entity.xijindicates the corresponding 0–1 decision variable, andMandNare the sizes ofG1andG2.

The objective of this model is given by (9), i.e., to maximize the total similarity between the assigned entity pairs. The constraints are given by (10)–(12). Equation (10) requires that each entity ofG1can only be assigned to no more than one entity ofG2, while (11) assumes that an entity ofG2can only be assigned to no more than one entity ofG1. Equation (12)indicates thatxijis a binary variable that takes 1 if entityeiandejare aligned and 0 otherwise.

Typically, this IP problem involvesM×Ndecision variables andM+Nconstraints. When the scales of the PDKGs are too large, there will be too many decision variables, which greatly decreases the solving speed. To solve this problem, we propose retaining the decision variables corresponding to the top-ksimilarity scores in each row and each column and set the remaining variables to 0. This reduces the computational load without greatly affecting the accuracy, as shown in the following section.

IV. EMPIRICAL EVALUATIONS

In this section, experiments are conducted to verify our proposed model on three cross-lingual datasets and a pair of PDKGs. The experimental settings, evaluation metrics, and results and analysis are provided in the following.

A. Experimental Setup

1) Datasets:To fully compare the performance of the proposed model and existing methods, we first carry out experiments on three commonly-used cross-lingual datasets from DBP15K [23], which were extracted from DBpedia containing multilingual versions of DBPZH-EN(Chinese to English),DBPJA-EN(Japanese to English), and DBPFR-EN(French to English). There are two similar KGs from different versions of DBpedia and 15 000 equivalent entities in each dataset.Table III lists the statistical summaries of these KGs. It can be seen from the statistical data that FR-EN is the densest dataset and KGs in the ZH-EN dataset have the biggest difference.Consistent with existing works, we randomly sample 30 percent of entity pairs for training and 70 percent for testing each time. The reported results are the average of 10 runs with different data splits to ensure unbiased evaluation.

STATISTICS TOAF BBLDEP 1II5IK DATASET

We conduct comprehensive comparisons with both baselines that only utilize structural information and methods that use multi-type information. It is worth noting that all of the baseline methods are based on supervised or semi-supervised techniques that use labeled data.

B. Results and Analysis

We obtain the metric reports of the compared baselines on the new dataset splits with the source code and parameter settings introduced in the original papers. The experimental results of the compared entity alignment solutions are shown in Table IV. These solutions can also be categorized into two groups according to whether using the iterative training strategy. The first category includes methods that do not employ the iterative training strategy, i.e., MTransE, KECG, AliNet,RSN, JAPE, GCN-Align, VR-GCN, GM-Align, and GMEHD-JEA, while the rest of the methods employ the bootstrapping strategy to enhance alignment performance. It can be seen that our IPEA model performs better than compared baselines on all datasets. The experimental results also suggest that the similarity matrix learned from the feature generation and adaptive feature fusion modules are more accurate than most baseline models as it achieved better alignment results onHits@10 and MRR based on independent prediction from the similarity matrix.

From the comparisons between MTransE and KECG that both only utilize structural information, we can see that TransE-based structural representation learning methods per-form worse than GCN-based embedding methods because TransE-based methods learn embeddings in different vector spaces, which suffer from information loss when matching entities in different embedding spaces in spite of space projection. Therefore, we devise a GCN-based KG embedding model to learn entities’ and relations’ structural representations. The proposed KGAT model can not only learn embeddings of different KGs into the same vector space, but also can model rich structural semantics between entities and relations.We also perform experiments to demonstrate the effectiveness of the proposed graph attention mechanism. We compare the proposed KGAT module with the GAT-based KECG model with the same parameter settings and the same name embeddings to initialize entities’ embeddings for fairness. We report the results in Table V. The results demonstrate that the proposed KGAT model outperforms the KECG model by explicitly incorporating entities and relations into a unified model. Although some more complicated GCNs like AliNet could achieve better performance by aggregating distant neighbors, they suffer from heavy computation burden and cannot learn the relation embeddings explicitly, and thus cannot effectively model entities’ relational similarities.

TABLE IV RESULT COMPARISON ON ENTITY ALIGNMENT

In the proposed IPEA model, we adopt the bootstrapping strategy to improve final performance by fully exploiting the highly confident alignment predictions. As is shown in Fig. 6,the performance of different modules in IPEA changes with iterative training. From the results, we can see that all themodules benefit from the enrichment of alignment seeds since their performance increases with iterative training. We can also see that their performance converges quickly and only two epochs are required to reach the highest performance level. These results also prove our model’s excellent convergence.

TABLE V COMPARATIVE STUDY OF KECG AND KGAT

Most baseline methods identify equivalent entity pairs independently, which make them easy to obtain many-to-one alignment results. Although a few recent methods align entities with the one-to-one constraint by formulating one-to-one entity alignment as a stable matching problem and solving it with the DAA method, we propose that this is sub-optimal as it ignores the differences in similarity scores between two groups of entity pairs. To evaluate our proposed IP-based collective counterpart assignment method, we compare it with the independent and DAA strategies based on the same similarity matrix. As can be seen from Fig. 7, our proposed IP strategy achieves the best performance and improves upon DAA by at least 2.2% on all datasets. The results demonstrate the effectiveness of collectively considering all entity pairs while assigning counterparts. In addition to the one-to-one constraint, the proposed IP strategy considers that the candidate with a higher similarity score is more likely to be the equivalent entity if multiple candidates compete for the same entity, and thus, is more optimized.

Fig. 6. Hits@1 results with respect to training iterations. Our model benefits from iterative training and converges quickly.

Fig. 7. Entity alignment results of different counterpart assignment strategies. The proposed IP-based alignment strategy achieves the best performance.

We also conduct an ablation study on the three datasets to evaluate each module’s effectiveness, and results are reported in Table VI. From the results, we can see that the adaptive fusion of different kinds of similarities (IPEA vs. IPEA w/o AFF) contributes greatly to the proposed model’s performance as it drops by more than 10% if we simply add the three similarities. We then examine the effectiveness of the IP-based collective counterpart assignment mechanism (IPEA vs. IPEA w/o IP) in our model. We can see thatHits@1 drops dramatically if we independently assign counterparts without considering the consistency and exclusiveness constraints,which demonstrates that the collective counterpart assignment strategy plays a part in IPEA. The comparisons (IPEA vs. IPEA w/o Iter) also demonstrate the usefulness of iterative training and pre-alignment seed enrichment.

C. Parameter Sensitivity

We conduct experiments to evaluate the effect of regularization in (4). Three most frequently used regularizationsincluding dropout, L1 normalization, and L2 normalization are evaluated for the KGAT model. The results are shown in Fig. 8. For dropout regularization, we set the dropout rate from 0.0 to 0.5. KGAT with a 0.2 dropout rate achieves the best performance on the ZH-EN dataset, while for the other two datasets, its performance drops with the increase of dropout rate. The weights of L1 normalization and L2 normalization are set from 0 to 0.1. We can see that these two regularizations do not impact KGAT’s performance significantly and the optimal normalization weights are different for different datasets.

TABLE VI EXPERIMENT RESULTS OF ABLATION

Sensitivity to the number of alignment seeds is an important metric for measuring the performance of an entity alignment model as it is costly and time-consuming to prepare large number of seeds manually. Following [36], we conduct experiments with 10% to 40% training seeds to investigate the sensitivity of our proposed IPEA to the proportion of initial seeds. Fig. 9 shows the performances of our IPEA and some best-performed baseline methods. From the results, we can see that IPEA performs better than other methods under all experimental settings on all datasets and the results of all methods gradually improve with the increase of pre-alignment seeds as expected. However, our model outperforms most of the baseline methods with regards to sensitivity to training seeds as theHits@1 of most methods decrease dramatically if the number of alignment seeds decreases. The advantages of IPEA are more obvious with fewer training seeds as it still achieves excellent performance with only 10% of total alignments for training. The results indicate that IPEA can learn more useful information with limited alignment seeds, resulting in its robustness and applicability to large-scale real-world KGs.This is mainly because the proposed model provides better similarities in the case where there are few alignment seeds using adaptive fusion of the seed-independent attribute similarities. It can also enrich the training seeds with highly confident predictions, which reduces its requirement for a lot of training data.

Fig. 8. Hits@1 results of KGAT with different regularizations. Regularization may be helpful for the KGAT model, but the parameters must be carefully selected and the optimal hyper-parameters for different datasets are different.

Fig. 9. Hits@1 results with respect to the proportion of pre-alignment seeds. The proposed model is more robust to pre-alignment seeds and performs best with few labeled seeds.

As can be seen from Fig. 10, the performance of IPEA varies with the number of candidates considered for each entity, i.e,k, while assigning counterparts in the IP-based decision making process. With the increase ofk, the entity alignment accuracy of IPEA increases gradually as it collectively considers more candidates and the results may be closer to a higherHits@k. Whenkexceeds a certain value that is less than 20, the performance of IPEA does not change by a lot.This indicates that we do not need to model large-scale IP tasks to obtain satisfactory alignment results, which is suitable for large-scale entity alignment problems.

Fig. 10. Entity alignment results with respect to the number of candidates(k) considered in the IP-based counterpart assignment module. Performance increases with the increase of candidates collectively considered while aligning entities.

D. Case Study

A case study is conducted to examine the performance of IPEA on real PDKGs and propose possible applications of entity alignment-based knowledge fusion on power grid dispatching. We utilize the PDKG proposed by Daiet al. [14] to construct the dataset, which is generated from dispatching simulation data of the IEEE 39 nodes standard example. In this PDKG, triple (h,r,t) represents the state of the power grid changing fromhtotwith actionr. It is noted that two states may belong to the same entity since they may be equivalent in physical sense. Therefore, the authors proposed grouping power grid states into a few entities based on the decision tree method. Each state is represented by a 116-dimensional state index in which each dimension represents the electrical state of a line or a device, and the attributes of an entity is the average of the states in this entity. Based on the fundamental PDKG, we generate a distributed copy which is a similar but slightly different PDKG to align by randomly dropping 20%of the edges and adding Gaussian noise with a mean value of 0.05 to the attributes, as done in [50].

We compare our model on the entity alignment of PDKGs with two best-performed methods, i.e., DAT and CEA, to evaluate its performance. All three methods utilize the structural, attribute, and relational information to calculate entities’similarities. The experimental results with different proportions of initial alignments are shown in Fig. 11. The results demonstrate that the proposed IPEA outperforms baseline methods, and the results prove its strong ability to integrate different information and making more accurate collective decisions for the knowledge fusion of PDKGs. The results also indicate that CEA performs worse than DAT on PDKGs.This is because the attribute information of PDKGs is more noisy than that of cross-lingual KGs and simply combining entities’ similarities with different information cannot effectively eliminate the influence of noise, which in turn demonstrates the effectiveness of adaptively integrating different information.

Fig. 11. Entity alignment results on PDKGs. The proposed IPEA achieves the state-of-the-art performance.

PDKGs provide a useful knowledge-based tool for automated power dispatching and intelligent services and help dispatchers to make better power dispatching operations [13].The knowledge fusion of multiple PDKGs based on entity alignment can effectively improve the completeness of each PDKG and provide more accurate knowledge supports. The following applications can be developed by the knowledge fusion of PDKGs to develop future intelligent power grid dispatching systems. Firstly, feasible dispatching strategies can be recommended to the dispatcher based on the relation path generated from PDKGs, which provides an explainable human-machine cooperative dispatching approach. Secondly,some intelligent services like fault warning can be provided by monitoring the state transition in PDKGs. Thirdly, the fused PDKGs can also provide knowledge for the learning of machine dispatchers. For example, various reinforcement learning agents have been developed for the automatic dispatching. However, agents have difficulty in learning safe and effective policies in such tasks due to their complex environments and huge decision spaces. To overcome this problem,researchers have proposed assisting agents’ learning with knowledge learned from supervised learning, which leads to reinforcement learning with the supervision from demonstration. It has been proven that structured knowledge can help agents learn more effective strategies and converge faster.

E. Discussion

The proposed IPEA model is a collective entity alignment model for the knowledge fusion of PDKGs, in which a novel knowledge graph representation learning model is proposed to learn the embeddings of entities and relations explicitly and an IP-based collective counterpart assignment method is designed. With these designs, IPEA achieves state-of-the-art performance on the entity alignment task for both cross-lingual KGs and PDKGs. In particular, the KGAT module enables the model to learn the correlations between entities and relations explicitly with their embeddings. With these embeddings,relations are aligned and the structural, attribute, and relational similarities are effectively calculated and integrated by the co-attention network. In the end, one-to-one alignments are obtained based on the counterpart assignment module considering both consistency and exclusiveness constraints. The proposed model can also be used to solve the equivalent node identification of other graphs like social networks. For example, the linkage of accounts belonging to the same user between Facebook and Twitter is helpful for some downstream applications such as social recommendation.

However, the entity alignment of PDKGs is not robust to noise in attributes, which is mainly because these attributes are the average of groups of power states and there may be a large drift between the attributes of equivalent entities. Therefore, the attributes need to be further refined while constructing PDKGs to better characterize entities and capture the key features of different states in semantic. For example, the attribute features representing different entities should be extracted and a representation learning system to extract the common attributes of a group of states should be carefully designed. Furthermore, the applications of PDKGs especially the knowledge fusion of multiple complementary PDKGs have not been studied. In the future, we will focus on integrating multiple PDKGs to generate more accurate dispatching recommendations and assist agents’ learning.

V. CONCLUSION

In this paper, we propose a novel entity alignment model for the knowledge fusion of PDKGs, which integrates structural,attribute, and relational information to measure entities’ similarities and collectively assigns counterparts with consistency and exclusiveness constraints. We first learn entities’ and relations’ representations based on a novel graph attention model and align relations based on their embeddings. Then, entities’connected relation types are encoded into fixed-length vectors to model their relational similarities. We then apply a coattention mechanism to integrate the structural, attribute, and relational representations to calculate the similarities between any pairs of entities. We also propose an IP-based collective counterpart assignment mechanism to solve the alignment problem with one-to-one constraint and add highly confident predictions to the alignment seeds to iteratively improve the performance. Compared with existing embedding-based models, our proposed model performs consistently better on both PDKGs and commonly used cross-lingual KGs, and comparisons from the ablation study also demonstrate the usefulness of designed modules.

However, the robustness to attribute noises of the proposed model still needs to be improved and applications of PDKGs remain to be explored. To address these issues, in the future,we are interested in designing effective attribute representation learning methods to improve overall entity alignment performance. Effective methods to extract knowledge from the fusion of multiple PDKGs to generate dispatching strategies and improve the performance of reinforcement learning models are also important directions.