Title: Complex and Holographic Embeddings of Knowledge Graphs: A Comparison,
Abstract: Embeddings of knowledge graphs have received significant attention due to
their excellent performance for tasks like link prediction and entity
resolution. In this short paper, we are providing a comparison of two
state-of-the-art knowledge graph embeddings for which their equivalence has
recently been established, i.e., ComplEx and HolE [Nickel, Rosasco, and Poggio,
2016; Trouillon et al., 2016; Hayashi and Shimbo, 2017]. First, we briefly
review both models and discuss how their scoring functions are equivalent. We
then analyze the discrepancy of results reported in the original articles, and
show experimentally that they are likely due to the use of different loss
functions. In further experiments, we evaluate the ability of both models to
embed symmetric and antisymmetric patterns. Finally, we discuss advantages and
disadvantages of both models and under which conditions one would be preferable
to the other.