Abstract

Knowledge Graph (KG) embedding has emerged as a very active area of research over the last few years, resulting in the development of several embedding methods. These KG embedding methods represent KG entities and relations as vectors in a high-dimensional space. Despite this popularity and effectiveness of KG embeddings in various tasks (e.g., link prediction), geometric understanding of such embeddings (i.e., arrangement of entity and relation vectors in vector space) is unexplored – we fill this gap in the paper. We initiate a study to analyze the geometry of KG embeddings and correlate it with task performance and other hyperparameters. To the best of our knowledge, this is the first study of its kind. Through extensive experiments on real-world datasets, we discover several insights. For example, we find that there are sharp differences between the geometry of embeddings learnt by different classes of KG embeddings methods. We hope that this initial study will inspire other follow-up research on this important but unexplored problem.

Highlights

  • Knowledge Graphs (KGs) are multi-relational graphs where nodes represent entities and typededges represent relationships among entities

  • Through extensive analysis, we discover several interesting insights about the geometry of KG embeddings

  • In this paper we focus on understanding the geometry of KG embeddings

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Summary

Introduction

Knowledge Graphs (KGs) are multi-relational graphs where nodes represent entities and typededges represent relationships among entities Recent research in this area has resulted in the development of several large KGs, such as NELL (Mitchell et al, 2015), YAGO (Suchanek et al, 2007), and Freebase (Bollacker et al, 2008), among others. The problem of learning embeddings for Knowledge Graphs has received significant attention in recent years, with several methods being proposed (Bordes et al, 2013; Lin et al, 2015; Nguyen et al, 2016; Nickel et al, 2016; Trouillon et al, 2016) These methods represent entities and relations in a KG as vectors in high dimensional space. All these methods employ a score function for distinguishing correct triples from incorrect ones

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