SimE: A Knowledge Graph Embedding Model to Encode Self-Similar Structures Through Algebraic and Geometric Transformations

Knowledge Graphs (KGs), with their intricate hierarchies and semantic relationships, present unique challenges for graph representation learning, necessitating tailored approaches to effectively capture and encode their complex structures into useful numerical representations. The fractal-like nature of these graphs, where patterns repeat at various scales and complexities, requires specialized algorithms that can adapt and learn from the multi-level structures inherent in the data. This similarity to fractals requires methods that preserve the recursive detail of knowledge graphs while facilitating efficient learning and extraction of relational patterns. In this study, we explore the integration of similarity group with attention mechanisms to represent knowledge graphs in complex spaces. In our approach, SimE, we make use of the algebraic (bijection) and geometric (similarity) properties of the similarity transformations to enhance the representation of self-similar fractals in KGs. We empirically validate the capability of providing representations of bijections and similarities in benchmark KGs. We also conducted controlled experiments that captured one-to-one, one-to-many, and many-to-many relational patterns and studied the behavior of state-of-the-art models including the proposed SimE model. Because of the lack of benchmark fractal-like KG datasets, we created a set of fractal-like testbeds to assess the subgraph similarity learning ability of models. The observed results suggest that SimE captures the complex geometric structures of KGs whose statements satisfy these algebraic and geometric properties. In particular, SimE is competitive with state-of-the-art KG embedding models and is able to achieve high values of Hits@1. As a result, SimE is capable of effectively predicting correct links and ranking them with the highest ranks. SimE is publicly available on GitHub https://github.com/NIMI-research/SimE.