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Ultrahyperbolic Knowledge Graph Embeddings

Bo Xiong, Shichao Zhu, Mojtaba Nayyeri, Chengjin Xu, Shirui Pan, Chuan Zhou, Steffen Staab

ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), pp. 1–10, 2022.


Recent knowledge graph (KG) embeddings have been advanced by hyperbolic geometry due to its superior capability for representing hierarchies. The topological structures of real-world KGs, however, are rather heterogeneous, i.e., a KG is composed of multiple distinct hierarchies and non-hierarchical graph structures. Therefore, a homogeneous (either Euclidean or hyperbolic) geometry is not sufficient for fairly representing such heterogeneous structures. To capture the topological heterogeneity of KGs, we present an ultrahyperbolic KG embedding (UltraE) in an ultrahyperbolic (or pseudo-Riemannian) manifold that seamlessly interleaves hyperbolic and spherical manifolds. In particular, we model each relation as a pseudo-orthogonal transformation that preserves the pseudo-Riemannian bilinear form. The pseudo-orthogonal transformation is decomposed into various operators (i.e., circular rotations, reflections and hyperbolic rotations), allowing for simultaneously modeling heterogeneous structures as well as complex relational patterns. Experimental results on three standard KGs show that UltraE outperforms previous Euclidean- and hyperbolic-based approaches.



@inproceedings{xiong22_kdd, title = {Ultrahyperbolic Knowledge Graph Embeddings}, author = {Xiong, Bo and Zhu, Shichao and Nayyeri, Mojtaba and Xu, Chengjin and Pan, Shirui and Zhou, Chuan and Staab, Steffen}, year = {2022}, pages = {1--10}, booktitle = {ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD)} }