Knowledge Graph Completion via Complex Tensor Factorization

Abstract

In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices---thus all possible relation/adjacency matrices---are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.

38 pages, accepted in JMLR. This is an extended version of the article "Complex embeddings for simple link prediction" (ICML 2016)

References in corpus (5)

• Global Optimality of Local Search for Low Rank Matrix Recovery
• Matrix Completion has No Spurious Local Minimum
• Open Question Answering with Weakly Supervised Embedding Models
• On the Equivalence of Holographic and Complex Embeddings for Link Prediction
• Complex and Holographic Embeddings of Knowledge Graphs: A Comparison

Cited by in corpus (13)

• Ontology Reasoning with Deep Neural Networks
• Inductive Relation Prediction by Subgraph Reasoning
• Analysis of the Impact of Negative Sampling on Link Prediction in Knowledge Graphs
• Fast Linear Model for Knowledge Graph Embeddings
• Cognitive Knowledge Graph Reasoning for One-shot Relational Learning
• Complex and Holographic Embeddings of Knowledge Graphs: A Comparison
• Variational Knowledge Graph Reasoning
• Interstellar: Searching Recurrent Architecture for Knowledge Graph Embedding
• TorusE: Knowledge Graph Embedding on a Lie Group
• Efficient, Simple and Automated Negative Sampling for Knowledge Graph Embedding
• Information Extraction from Scientific Literature for Method Recommendation
• Explainable Deep RDFS Reasoner
• NePTuNe: Neural Powered Tucker Network for Knowledge Graph Completion