# 5* Knowledge Graph Embeddings with Projective Transformations

arXiv: https://arxiv.org/abs/2006.04986 · HTML: https://mlsanity.com/paper/2006.04986/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 19 of 19)

- [Ultrahyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.00449/) (2022)
- [Link Prediction with Attention Applied on Multiple Knowledge Graph Embedding Models](https://mlsanity.com/paper/2302.06229/) (2023)
- [KRACL: Contrastive Learning with Graph Context Modeling for Sparse Knowledge Graph Completion](https://mlsanity.com/paper/2208.07622/) (2022)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Applications of knowledge graphs for food science and industry](https://mlsanity.com/paper/2107.05869/) (2021)
- [Survey on English Entity Linking on Wikidata](https://mlsanity.com/paper/2112.01989/) (2021)
- [3D Human Pose Estimation Using M"obius Graph Convolutional Networks](https://mlsanity.com/paper/2203.10554/) (2022)
- [Knowledge Base Completion Meets Transfer Learning](https://mlsanity.com/paper/2108.13073/) (2021)
- [Rule Induction in Knowledge Graphs Using Linear Programming](https://mlsanity.com/paper/2110.08245/) (2021)
- [Expanding Expressivity in Transformer Models with M"obiusAttention](https://mlsanity.com/paper/2409.12175/) (2024)
- [Hyperbolic Hierarchical Knowledge Graph Embeddings for Link Prediction in Low Dimensions](https://mlsanity.com/paper/2204.13704/) (2022)
- [ConvD: Attention Enhanced Dynamic Convolutional Embeddings for Knowledge Graph Completion](https://mlsanity.com/paper/2312.07589/) (2023)
- [Ontology-Enhanced Knowledge Graph Completion using Large Language Models](https://mlsanity.com/paper/2507.20643/) (2025)
- [ReaLM: Residual Quantization Bridging Knowledge Graph Embeddings and Large Language Models](https://mlsanity.com/paper/2510.09711/) (2025)
- [Geometric Structural Knowledge Graph Foundation Model](https://mlsanity.com/paper/2512.22931/) (2025)
- [Pre-training and Diagnosing Knowledge Base Completion Models](https://mlsanity.com/paper/2401.15439/) (2024)
- [Sharing Parameter by Conjugation for Knowledge Graph Embeddings in Complex Space](https://mlsanity.com/paper/2404.11809/) (2024)
- [SMART: Relation-Aware Learning of Geometric Representations for Knowledge Graphs](https://mlsanity.com/paper/2507.13001/) (2025)
- [HyperComplEx: Adaptive Multi-Space Knowledge Graph Embeddings](https://mlsanity.com/paper/2511.10842/) (2025)

## Abstract (arXiv)

Performing link prediction using knowledge graph embedding models has become a popular approach for knowledge graph completion. Such models employ a transformation function that maps nodes via edges into a vector space in order to measure the likelihood of the links. While mapping the individual nodes, the structure of subgraphs is also transformed. Most of the embedding models designed in Euclidean geometry usually support a single transformation type - often translation or rotation, which is suitable for learning on graphs with small differences in neighboring subgraphs. However, multi-relational knowledge graphs often include multiple sub-graph structures in a neighborhood (e.g. combinations of path and loop structures), which current embedding models do not capture well. To tackle this problem, we propose a novel KGE model (5*E) in projective geometry, which supports multiple simultaneous transformations - specifically inversion, reflection, translation, rotation, and homothety. The model has several favorable theoretical properties and subsumes the existing approaches. It outperforms them on the most widely used link prediction benchmarks