The approach of knowledge graph embedding (KGE) enables it possible to represent facts of a knowledge graph (KG) in low-dimensional continuous vector spaces. Consequently, it can significantly reduce the complexity of those operations performed on the underlying KG, and has attracted a lot of attention in recent years. However, most of KGE approaches have only been developed over static facts and ignore the time attribute. As a matter of effect, in some real-world KGs, a fact might only be valid for a specific time interval or point in time. For instance, the fact (Barack Obama, is president of, US, [2009-2017]) is only valid between 2009 and 2017. To conquer this issue, based on a famous tensor factorization approach, canonical polyadic decomposition, we propose two new temporal KGE models called TSimplE and TNTSimplE that integrates time information besides static facts. A non-temporal component is also added to deal with heterogeneous temporal KGs that include both temporal and non-temporal relations. We prove that the proposed models are fully expressive which has a bound on the dimensionality of their embeddings, and can incorporate several important types of background knowledge including symmetry, antisymmetry and inversion. In addition, our models are capable of dealing with two common challenges in real-world temporal KGs, i.e., modeling time intervals and predicting time for facts with missing time information. We conduct extensive experiments on three real-world temporal KGs: ICEWS, YAGO3 and Wikidata. The results indicate that our models achieve start-of-the-art performance with lower time or space complexity.
