Knowledge Hypergraph Embedding Meets Relational Algebra
Authors: Bahare Fatemi, Perouz Taslakian, David Vazquez, David Poole; Volume 24, Issue 105, Pages 1-34, 2023.
Abstract
Relational databases have been successful in data storage and rely on query languages for information retrieval. These query languages are typically based on relational algebra, which is a mathematical formalization at the core of relational models. Knowledge graphs are flexible data storage structures that can be used for knowledge completion through machine learning techniques. Knowledge hypergraphs extend knowledge graphs by allowing multi-argument relations. This study explores the completion of knowledge hypergraphs using relational algebra and its core operations. We investigate whether these methods can capture high-level abstractions in terms of relational algebra operations. To address this, we introduce a simple embedding-based model called Relational Algebra Embedding (ReAlE) that performs link prediction in knowledge hypergraphs. Theoretical analysis shows that ReAlE is fully expressive and can represent the relational algebra operations of renaming, projection, set union, selection, and set difference. Experimental results demonstrate that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion and in representing each of these primitive relational algebra operations. Additionally, we generate a synthetic knowledge hypergraph and design an algorithm based on the Erdos-Rényi model for generating random graphs to conduct the latter experiment.
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