Geometric Relational Embeddings
This work addresses the limitation of existing relational embeddings for researchers and practitioners dealing with symbolic data in networks, knowledge graphs, and ontologies, offering a novel paradigm rather than an incremental improvement.
The paper tackled the problem of vector-based relational representation learning failing to capture complex symbolic structures, and proposed geometric relational embeddings that effectively model hierarchies, cycles, logical constraints, and high-order patterns in relational data, with results showing efficacy on benchmark and real-world datasets.
Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex and symbolic. We propose geometric relational embeddings, a paradigm of relational embeddings that respect the underlying symbolic structures. Specifically, this dissertation introduces various geometric relational embedding models capable of capturing: 1) complex structured patterns like hierarchies and cycles in networks and knowledge graphs; 2) logical structures in ontologies and logical constraints applicable for constraining machine learning model outputs; and 3) high-order structures between entities and relations. Our results obtained from benchmark and real-world datasets demonstrate the efficacy of geometric relational embeddings in adeptly capturing these discrete, symbolic, and structured properties inherent in relational data.