Knowledge graphs are useful for many artificial intelligence (AI) tasks. However, knowledge graphs often have missing facts. To populate the graphs, knowledge graph embedding models have been developed. Knowledge graph embedding models map entities and relations in a knowledge graph to a vector space and predict unknown triples by scoring candidate triples. TransE is the first translation-based method and it is well known because of its simplicity and efficiency for knowledge graph completion. It employs the principle that the differences between entity embeddings represent their relations. The principle seems very simple, but it can effectively capture the rules of a knowledge graph. However, TransE has a problem with its regularization. TransE forces entity embeddings to be on a sphere in the embedding vector space. This regularization warps the embeddings and makes it difficult for them to fulfill the abovementioned principle. The regularization also affects adversely the accuracies of the link predictions. On the other hand, regularization is important because entity embeddings diverge by negative sampling without it. This paper proposes a novel embedding model, TorusE, to solve the regularization problem. The principle of TransE can be defined on any Lie group. A torus, which is one of the compact Lie groups, can be chosen for the embedding space to avoid regularization. To the best of our knowledge, TorusE is the first model that embeds objects on other than a real or complex vector space, and this paper is the first to formally discuss the problem of regularization of TransE. Our approach outperforms other state-of-the-art approaches such as TransE, DistMult and ComplEx on a standard link prediction task. We show that TorusE is scalable to large-size knowledge graphs and is faster than the original TransE.
TransH @cite_0 projects entities on the hyperplane corresponding to a relation between them. Projection makes the model more flexible by choosing components of embeddings to represent each relation. TransR @cite_19 has a matrix for each relation and the entities are mapped by linear transformation that multiplies the matrix to calculate the score of a triple. TransR is considered as generalized TransH because projection is one of linear transformations. These models have an advantage in power of expression comparing with TransE. At the same time, however, they easily become overfitted.
@cite_0 @cite_19
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We deal with embedding a large scale knowledge graph composed of entities and relations into a continuous vector space. TransE is a promising method proposed recently, which is very efficient while achieving state-of-the-art predictive performance. We discuss some mapping properties of relations which should be considered in embedding, such as reflexive, one-to-many, many-to-one, and many-to-many. We note that TransE does not do well in dealing with these properties. Some complex models are capable of preserving these mapping properties but sacrifice efficiency in the process. To make a good trade-off between model capacity and efficiency, in this paper we propose TransH which models a relation as a hyperplane together with a translation operation on it. In this way, we can well preserve the above mapping properties of relations with almost the same model complexity of TransE. Additionally, as a practical knowledge graph is often far from completed, how to construct negative examples to reduce false negative labels in training is very important. Utilizing the one-to-many many-to-one mapping property of a relation, we propose a simple trick to reduce the possibility of false negative labeling. We conduct extensive experiments on link prediction, triplet classification and fact extraction on benchmark datasets like WordNet and Freebase. Experiments show TransH delivers significant improvements over TransE on predictive accuracy with comparable capability to scale up. Knowledge graph completion aims to perform link prediction between entities. In this paper, we consider the approach of knowledge graph embeddings. Recently, models such as TransE and TransH build entity and relation embeddings by regarding a relation as translation from head entity to tail entity. We note that these models simply put both entities and relations within the same semantic space. In fact, an entity may have multiple aspects and various relations may focus on different aspects of entities, which makes a common space insufficient for modeling. In this paper, we propose TransR to build entity and relation embeddings in separate entity space and relation spaces. Afterwards, we learn embeddings by first projecting entities from entity space to corresponding relation space and then building translations between projected entities. In experiments, we evaluate our models on three tasks including link prediction, triple classification and relational fact extraction. Experimental results show significant and consistent improvements compared to state-of-the-art baselines including TransE and TransH. The source code of this paper can be obtained from https: github.com mrlyk423 relation_extraction.