Complex and Holographic Embeddings of Knowledge Graphs: A Comparison

TL;DR

This paper compares two state-of-the-art knowledge graph embedding models, ComplEx and HolE, analyzing their equivalence, differences in reported results, and performance on symmetric and antisymmetric patterns.

Contribution

It provides a detailed comparison of ComplEx and HolE, clarifying their equivalence and analyzing factors affecting their performance.

Findings

Results discrepancies are likely due to different loss functions.

Both models can embed symmetric and antisymmetric patterns effectively.

Comparison highlights conditions favoring each model.

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.