# Geometric Algebra based Embeddings for Static and Temporal Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2202.09464 · HTML: https://mlsanity.com/paper/2202.09464/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 23 of 23)

- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [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)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [A Survey on Knowledge Graph-Based Recommender Systems](https://mlsanity.com/paper/2003.00911/) (2020)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Learning Sequence Encoders for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1809.03202/) (2018)
- [Tensor Decompositions for temporal knowledge base completion](https://mlsanity.com/paper/2004.04926/) (2020)
- [Diachronic Embedding for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1907.03143/) (2019)
- [InteractE: Improving Convolution-based Knowledge Graph Embeddings by Increasing Feature Interactions](https://mlsanity.com/paper/1911.00219/) (2019)
- [TeRo: A Time-aware Knowledge Graph Embedding via Temporal Rotation](https://mlsanity.com/paper/2010.01029/) (2020)
- [Node Embedding over Temporal Graphs](https://mlsanity.com/paper/1903.08889/) (2019)
- [Knowledge Base Completion: Baselines Strike Back](https://mlsanity.com/paper/1705.10744/) (2017)
- [Temporal Knowledge Base Completion: New Algorithms and Evaluation Protocols](https://mlsanity.com/paper/2005.05035/) (2020)
- [Embedding Models for Episodic Knowledge Graphs](https://mlsanity.com/paper/1807.00228/) (2018)
- [Temporal Knowledge Graph Embedding Model based on Additive Time Series Decomposition](https://mlsanity.com/paper/1911.07893/) (2019)
- [On Multi-Relational Link Prediction with Bilinear Models](https://mlsanity.com/paper/1709.04808/) (2017)
- [Knowledge Graph Embeddings in Geometric Algebras](https://mlsanity.com/paper/2010.00989/) (2020)
- [Time-aware Graph Embedding: A temporal smoothness and task-oriented approach](https://mlsanity.com/paper/2007.11164/) (2020)

## Built on by (most cited first, 6 of 6)

- [A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2308.02457/) (2023)
- [On the Evolution of Knowledge Graphs: A Survey and Perspective](https://mlsanity.com/paper/2310.04835/) (2023)
- [Incorporating Structured Sentences with Time-enhanced BERT for Fully-inductive Temporal Relation Prediction](https://mlsanity.com/paper/2304.04717/) (2023)
- [Neurosymbolic Methods for Dynamic Knowledge Graphs](https://mlsanity.com/paper/2409.04572/) (2024)
- [UniHR: Hierarchical Representation Learning for Unified Knowledge Graph Link Prediction](https://mlsanity.com/paper/2411.07019/) (2024)
- [Learning Granularity Representation for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2408.15293/) (2024)

## Abstract (arXiv)

Recent years, Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a Knowledge Graph (KG) into a geometric space and thus have gained increasing attentions. In addition, many recent Knowledge Graphs involve evolving data, e.g., the fact (textitObama, textitPresidentOf, textitUSA) is valid only from 2009 to 2017. This introduces important challenges for knowledge representation learning since such temporal KGs change over time. In this work, we strive to move beyond the complex or hypercomplex space for KGE and propose a novel geometric algebra based embedding approach, GeomE, which uses multivector representations and the geometric product to model entities and relations. GeomE subsumes several state-of-the-art KGE models and is able to model diverse relations patterns. On top of this, we extend GeomE to TGeomE for temporal KGE, which performs 4th-order tensor factorization of a temporal KG and devises a new linear temporal regularization for time representation learning. Moreover, we study the effect of time granularity on the performance of TGeomE models. Experimental results show that our proposed models achieve the state-of-the-art performances on link prediction over four commonly-used static KG datasets and four well-established temporal KG datasets across various metrics.