# Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces

arXiv: https://arxiv.org/abs/2211.03536 · HTML: https://mlsanity.com/paper/2211.03536/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 107 of its 243 references that are in the map.
- First posted on arXiv 7 Nov 2022.

## Builds on (most cited first, 30 of 107)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Leveraging Passage Retrieval with Generative Models for Open Domain Question Answering](https://mlsanity.com/paper/2007.01282/) (2020)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [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)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [ERNIE: Enhanced Language Representation with Informative Entities](https://mlsanity.com/paper/1905.07129/) (2019)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [QA-GNN: Reasoning with Language Models and Knowledge Graphs for Question Answering](https://mlsanity.com/paper/2104.06378/) (2021)
- [KEPLER: A Unified Model for Knowledge Embedding and Pre-trained Language Representation](https://mlsanity.com/paper/1911.06136/) (2019)
- [KGAT: Knowledge Graph Attention Network for Recommendation](https://mlsanity.com/paper/1905.07854/) (2019)
- [KG-BERT: BERT for Knowledge Graph Completion](https://mlsanity.com/paper/1909.03193/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)

## Built on by (most cited first, 30 of 41)

- [A Comprehensive Survey on Vector Database: Storage and Retrieval Technique, Challenge](https://mlsanity.com/paper/2310.11703/) (2023)
- [BEV-TSR: Text-Scene Retrieval in BEV Space for Autonomous Driving](https://mlsanity.com/paper/2401.01065/) (2024)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [HypKG: Hypergraph-based Knowledge Graph Contextualization for Precision Healthcare](https://mlsanity.com/paper/2507.19726/) (2025)
- [Automated Knowledge Graph Construction using Large Language Models and Sentence Complexity Modelling](https://mlsanity.com/paper/2509.17289/) (2025)
- [Large Language Model Enhanced Knowledge Representation Learning: A Survey](https://mlsanity.com/paper/2407.00936/) (2024)
- [Rethinking Regularization Methods for Knowledge Graph Completion](https://mlsanity.com/paper/2505.23442/) (2025)
- [Clinical Trial Recommendations Using Semantics-Based Inductive Inference and Knowledge Graph Embeddings](https://mlsanity.com/paper/2309.15979/) (2023)
- [Investigating Representation Universality: Case Study on Genealogical Representations](https://mlsanity.com/paper/2410.08255/) (2024)
- [A Survey of Link Prediction in N-ary Knowledge Graphs](https://mlsanity.com/paper/2506.08970/) (2025)
- [Cardinality Estimation on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2405.15231/) (2024)
- [HRGraph: Leveraging LLMs for HR Data Knowledge Graphs with Information Propagation-based Job Recommendation](https://mlsanity.com/paper/2408.13521/) (2024)
- [Large Language Models for Knowledge Graph Embedding: A Survey](https://mlsanity.com/paper/2501.07766/) (2025)
- [Can We Edit LLMs for Long-Tail Biomedical Knowledge?](https://mlsanity.com/paper/2504.10421/) (2025)
- [CiteFusion: An Ensemble Framework for Citation Intent Classification Harnessing Dual-Model Binary Couples and SHAP Analyses](https://mlsanity.com/paper/2407.13329/) (2024)
- [Knowledge Graph Embeddings: A Comprehensive Survey on Capturing Relation Properties](https://mlsanity.com/paper/2410.14733/) (2024)
- [Aligning Generalisation Between Humans and Machines](https://mlsanity.com/paper/2411.15626/) (2024)
- [Knowledge Graphs are not Created Equal: Exploring the Properties and Structure of Real KGs](https://mlsanity.com/paper/2311.06414/) (2023)
- [Context-aware knowledge graph framework for traffic speed forecasting using graph neural network](https://mlsanity.com/paper/2407.17703/) (2024)
- [Detecting Masquerade Attacks in Controller Area Networks Using Graph Machine Learning](https://mlsanity.com/paper/2408.05427/) (2024)
- [Diffusion-based Hierarchical Negative Sampling for Multimodal Knowledge Graph Completion](https://mlsanity.com/paper/2501.15393/) (2025)
- [A Systematic Evaluation of Knowledge Graph Embeddings for Gene-Disease Association Prediction](https://mlsanity.com/paper/2504.08445/) (2025)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [Flow-Modulated Scoring for Semantic-Aware Knowledge Graph Completion](https://mlsanity.com/paper/2506.23137/) (2025)
- [Relation Geometry in Semantic Space of Language Models](https://mlsanity.com/paper/2607.26762/) (2026)
- [Learning with Geometry: Including Riemannian Geometric Features in Coefficient of Pressure Prediction on Aircraft Wings](https://mlsanity.com/paper/2401.09452/) (2023)
- [DELE: Deductive EL++ Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/2411.01574/) (2024)
- [Domain and Range Aware Synthetic Negatives Generation for Knowledge Graph Embedding Models](https://mlsanity.com/paper/2411.14858/) (2024)
- [A Decade of Deep Learning: A Survey on The Magnificent Seven](https://mlsanity.com/paper/2412.16188/) (2024)
- [FAIRTOPIA: Envisioning Multi-Agent Guardianship for Disrupting Unfair AI Pipelines](https://mlsanity.com/paper/2506.09107/) (2025)

## Abstract (arXiv)

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.