Weakly-supervised Knowledge Graph Alignment with Adversarial Learning

This paper studies aligning knowledge graphs from different sources or languages . Most existing methods train supervised methods for the alignment , which usually require a large number of aligned knowledge triplets . However , such a large number of aligned knowledge triplets may not be available or are expensive to obtain in many domains . Therefore , in this paper we propose to study aligning knowledge graphs in fully-unsupervised or weakly-supervised fashion , i.e. , without or with only a few aligned triplets . We propose an unsupervised framework to align the entity and relation embddings of different knowledge graphs with an adversarial learning framework . Moreover , a regularization term which maximizes the mutual information between the embeddings of different knowledge graphs is used to mitigate the problem of mode collapse when learning the alignment functions . Such a framework can be further seamlessly integrated with existing supervised methods by utilizing a limited number of aligned triples as guidance . Experimental results on multiple datasets prove the effectiveness of our proposed approach in both the unsupervised and the weakly-supervised settings . 1 INTRODUCTION . Knowledge graphs represent a collection of knowledge facts and are quite popular in the real world . Each fact is represented as a triplet ( h , r , t ) , meaning that the head entity h has the relation r with the tail entity t. Examples of real-world knowledge graphs include instances which contain knowledge facts from general domain ( e.g. , Freebase 1 , WordNet 2 ) or facts from specific domains such as biomedical ontology ( e.g. , UMLS 3 ) . Knowledge graphs are critical to a variety of applications such as question answering ( Bordes et al. , 2014 ) and semantic search ( Guha et al. , 2003 ) . Research on knowledge graphs is attracting growing interest recently in both academia and industry communities . In practice , each knowledge graph is usually constructed from a single source or language , the coverage of which is limited . To enlarge the coverage and construct more unified knowledge graphs , a natural idea is to integrate multiple knowledge graphs from different sources or languages ( Arens et al. , 1993 ) . However , different knowledge graphs use distinct symbol systems to represent entities and relations , which are not compatible . Therefore , it is critical to align the entities and relations across different knowledge graphs ( a.k.a. , knowledge graph alignment ) before integrating them . Recently , many methods have been proposed to align entities and relations from a source knowledge graph to a target knowledge graph ( Zhu et al. , 2017a ; Chen et al. , 2017a ; b ; Sun et al. , 2018a ) . These methods first represent the entities and relations in low-dimensional spaces and then learn mapping functions to align the entities and relations from the source knowledge graph to the target one . Though these methods are proven quite effective , they rely on a large number of aligned triplets for training supervised alignment models , and such aligned triplets may not be available or can be expensive to obtain . As a result , the performance of these methods will be comprised . Therefore , it would be desirable to design an unsupervised or weakly-supervised approach for knowledge graph alignment , which requires a few or even without aligned triplets . 1 https : //developers.google.com/freebase/ 2 https : //wordnet.princeton.edu/ 3 https : //www.nlm.nih.gov/research/umls/ In this paper , we propose an unsupervised approach to knowledge graph alignment with adversarial training ( Goodfellow et al. , 2014 ) . Our proposed approach first represents the entities and relations in low-dimensional spaces with existing knowledge graph embedding methods ( e.g. , TransE ( Bordes et al. , 2013 ) ) and then learns alignment functions , i.e. , pe ( et|es ) and pr ( rt|rs ) , to map the entities and relations ( es and rs ) from the source knowledge graph to those ( et and rt ) in the target graph . Intuitively , an ideal alignment function is able to map all triples in the source graph to valid ones in the target graph . Therefore , we train a triplet discriminator to distinguish between the real triplets in the target graph and those aligned ones from the source graph . Such a discriminator measures the plausibility of a triplet in the target graph and provides a reward function for optimizing the alignment functions , which are optimized to fool the discriminator . The above process naturally forms an adversarial training procedure . By alternatively optimizing the alignment functions and the discriminator , the whole process can constantly enhance the alignment functions . Despite the effectiveness of adversarial learning in many scenarios , one big problem it may suffer from is the mode collapse ( Salimans et al. , 2016 ) . Specifically , in our case , it means that many entities in the source knowledge graph are aligned to only a few entities in the target knowledge graph . We propose to mitigate this problem by maximizing the mutual information between the entities in the source graph and those aligned entities , which can be effectively and effectively optimized with some recent techniques on mutual information neural estimation ( Belghazi et al. , 2018 ) . We further prove that by maximizing the mutual information , different source-graph entities are encouraged to be aligned to different target-graph entities , which mitigates the mode collapse . The whole framework can also be seamlessly integrated with existing supervised methods , in which we can use a few aligned entities or relations as guidance , yielding a weakly-supervised approach . Our approach can be effectively optimized with stochastic gradient descent , where the gradient for the alignment functions is calculated by the REINFORCE algorithm ( Williams , 1992 ) . We conduct extensive experiments on several datasets . Experimental results prove the effectiveness of our proposed approach in both the weakly-supervised and unsupervised settings . 2 RELATED WORK . Our work is related to knowledge graph embedding , which represents entities and relations as lowdimensional vectors ( a.k.a. , embedding ) . A variety of approaches have been proposed ( Bordes et al. , 2013 ; Wang et al. , 2014 ; Yang et al. , 2014 ; Sun et al. , 2018b ) , which can effectively preserve the similarities of entities and relations into the learned embeddings . We treat these techniques as tools to learn entity and relation embeddings , which serve as features for knowledge graph alignment . In literature , there are also some studies focusing on knowledge graph alignment . Most of them perform alignment by considering contextual features of entities and relations , such as their names ( Lacoste-Julien et al. , 2013 ) or text descriptions ( Chen et al. , 2018 ; Wang et al. , 2012 ; 2013 ) . However , such contextual features are not always available , and therefore these methods can not generalize to most knowledge graphs . In this paper , we consider the most general case , in which only the triplets in knowledge graphs are used for alignment . The studies most related to ours are Zhu et al . ( 2017a ) , Chen et al . ( 2017a ) and Sun et al . ( 2018a ) . Similar to our approach , they treat the entity and relation embeddings as features , and jointly train an alignment model . However , they totally rely on the labeled data ( e.g. , aligned entities ) to train the alignment model , whereas our approach incorporates additional signals by using adversarial training , and therefore achieves better results in the weakly-supervised and unsupervised settings . More broadly , our work belongs to the family of domain alignment , which aims at mapping data from one domain to the other domain . With the success of generative adversarial networks ( Goodfellow et al. , 2014 ) , many researchers have been bringing the idea to domain alignment , getting impressive results in many applications , such as image-to-image translation ( Zhu et al. , 2017b ; c ) , word-to-word translation ( Conneau et al. , 2017 ) and text style transfer ( Shen et al. , 2017 ) . These studies typically train a domain discriminator to distinguish between data points from different domains , and then the alignment function is optimized by fooling the discriminator . Our approach shares similar idea , but is designed with some specific intuitions in knowledge graphs . Besides , our work is also related to recent studies on neural mutual information estimation ( Belghazi et al. , 2018 ) , which estimate the mutual information of two distributions by using neural networks . Such a technique has been utilized in many applications , including image classification ( Hjelm et al. , 2018 ) and unsupervised node representation learning ( Veličković et al. , 2018 ) . All these studies use the technique to improve representation learning ( e.g. , image representation , node representation ) . In contrast , our approach uses the technique to avoid mode collapse in adversarial learning . Finally , Cai & Wang ( 2018 ) propose a method called KBGAN recently , which uses adversarial learning for generating negative examples in knowledge graph embedding algorithms . Compared with this work , both our method and KBGAN use the adversarial learning framework , but our work is fundamentally different from KBGAN . More specifically , the goal of KBGAN is to use adversarial learning to generate effective negative samples for knowledge graph embedding , while our work studies a very different problem , that is , knowledge graph alignment . We use the adversarial learning framework to learn effective mapping functions to align entities and relations across different knowledge graphs . Moreover , a major challenge in knowledge graph alignment is that the entities ( or relations ) in the source knowledge graph could be mapped to only a subset of entities ( or relations ) in the target knowledge graph . We propose to maximize the mutual information between the source entities ( relations ) and the mapped entities ( relations ) to mitigate this problem . 3 PROBLEM DEFINITION . Definition 1 ( KNOWLEDGE GRAPH . ) A knowledge graph is denoted as G = ( E , R , X ) , where E is a set of entities , R is a set of relations and X is a set of triplets . Each triplet x = ( h , r , t ) consists of a head entity h , a relation r and a tail entity t , meaning h has relation r with t. In practice , the coverage of each individual knowledge graph is usually limited , since it is typically constructed from a single source or language . To construct knowledge graphs with broader coverage , a straightforward way is to integrate multiple knowledge graphs from different sources or languages . However , each knowledge graph uses a unique symbol system to represent entities and relations , which is not compatible with other knowledge graphs . Therefore , a prerequisite for knowledge graph integration is to align entities and relations across different knowledge graphs ( a.k.a. , knowledge graph alignment ) . In this paper , we study how to align entities and relations from a source knowledge graph to those in a target knowledge graph , and the problem is formally defined below : Definition 2 ( KNOWLEDGE GRAPH ALIGNMENT . ) Given a source knowledge graph Gs = ( Es , Rs , Xs ) and a target knowledge graph Gt = ( Et , Rt , Xt ) , we aim at learning an entity alignment function pe and a relation alignment function pr . Given an entity es in the source graph and an entity et in the target graph , pe ( et|es ) gives the probability that es aligns to et . Similarly , for a source relation rs and a target relation rt , pr ( rt|rs ) gives the probability that rs aligns to rt .

Summary: The authors propose an unsupervised knowledge graph alignment framework, KAGAN, using adversarial training. Specifically, they utilize a triple discriminator to discriminate the aligned source triples and target triples, and a reward function to minimize the divergence between source triples and target triples. Also, they propose to leverage the lower bound of the mean KL divergence (mutual information) to resolve the mode collapse problem. The proposed method can be incorporated with a supervised method to be a weakly-supervised approach. Even though there are a family of unsupervised approaches for domain alignment, this paper is the first to solve the knowledge graph alignment problem in an unsupervised/weakly supervised way.