# Dual-Geometric Space Embedding Model for Two-View Knowledge Graphs

arXiv: https://arxiv.org/abs/2209.08767 · HTML: https://mlsanity.com/paper/2209.08767/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 18 of 18)

- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Spherical Text Embedding](https://mlsanity.com/paper/1911.01196/) (2019)
- [Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones](https://mlsanity.com/paper/2110.14923/) (2021)
- [Universal Representation Learning of Knowledge Bases by Jointly Embedding Instances and Ontological Concepts](https://mlsanity.com/paper/2103.08115/) (2021)
- [A Self-supervised Mixed-curvature Graph Neural Network](https://mlsanity.com/paper/2112.05393/) (2021)
- [Knowledge Association with Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2010.02162/) (2020)
- [HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/1908.04895/) (2019)
- [Switch Spaces: Learning Product Spaces with Sparse Gating](https://mlsanity.com/paper/2102.08688/) (2021)
- [Question-Answer Sentence Graph for Joint Modeling Answer Selection](https://mlsanity.com/paper/2203.03549/) (2022)

## Built on by (most cited first, 12 of 12)

- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [KABB: Knowledge-Aware Bayesian Bandits for Dynamic Expert Coordination in Multi-Agent Systems](https://mlsanity.com/paper/2502.07350/) (2025)
- [UUKG: Unified Urban Knowledge Graph Dataset for Urban Spatiotemporal Prediction](https://mlsanity.com/paper/2306.11443/) (2023)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Concept2Box: Joint Geometric Embeddings for Learning Two-View Knowledge Graphs](https://mlsanity.com/paper/2307.01933/) (2023)
- [Towards Enhancing Relational Rules for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2310.13411/) (2023)
- [Non-Euclidean Mixture Model for Social Network Embedding](https://mlsanity.com/paper/2411.04876/) (2024)
- [Know2BIO: A Comprehensive Dual-View Benchmark for Evolving Biomedical Knowledge Graphs](https://mlsanity.com/paper/2310.03221/) (2023)
- [Embedding Ontologies via Incorporating Extensional and Intensional Knowledge](https://mlsanity.com/paper/2402.01677/) (2024)
- [Proficient Graph Neural Network Design by Accumulating Knowledge on Large Language Models](https://mlsanity.com/paper/2408.06717/) (2024)
- [Combining Euclidean and Hyperbolic Representations for Node-level Anomaly Detection](https://mlsanity.com/paper/2510.11827/) (2025)
- [Biquaternionic Space with Complex-valued Attention for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2609.14279/) (2026)

## Abstract (arXiv)

Two-view knowledge graphs (KGs) jointly represent two components: an ontology view for abstract and commonsense concepts, and an instance view for specific entities that are instantiated from ontological concepts. As such, these KGs contain heterogeneous structures that are hierarchical, from the ontology-view, and cyclical, from the instance-view. Despite these various structures in KGs, most recent works on embedding KGs assume that the entire KG belongs to only one of the two views but not both simultaneously. For works that seek to put both views of the KG together, the instance and ontology views are assumed to belong to the same geometric space, such as all nodes embedded in the same Euclidean space or non-Euclidean product space, an assumption no longer reasonable for two-view KGs where different portions of the graph exhibit different structures. To address this issue, we define and construct a dual-geometric space embedding model (DGS) that models two-view KGs using a complex non-Euclidean geometric space, by embedding different portions of the KG in different geometric spaces. DGS utilizes the spherical space, hyperbolic space, and their intersecting space in a unified framework for learning embeddings. Furthermore, for the spherical space, we propose novel closed spherical space operators that directly operate in the spherical space without the need for mapping to an approximate tangent space. Experiments on public datasets show that DGS significantly outperforms previous state-of-the-art baseline models on KG completion tasks, demonstrating its ability to better model heterogeneous structures in KGs.