# HousE: Knowledge Graph Embedding with Householder Parameterization

arXiv: https://arxiv.org/abs/2202.07919 · HTML: https://mlsanity.com/paper/2202.07919/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 16 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Knowledge Base Completion: Baselines Strike Back](https://mlsanity.com/paper/1705.10744/) (2017)
- [TransA: An Adaptive Approach for Knowledge Graph Embedding](https://mlsanity.com/paper/1509.05490/) (2015)
- [Rot-Pro: Modeling Transitivity by Projection in Knowledge Graph Embedding](https://mlsanity.com/paper/2110.14450/) (2021)

## Built on by (most cited first, 29 of 29)

- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Knowledge Graph Contrastive Learning Based on Relation-Symmetrical Structure](https://mlsanity.com/paper/2211.10738/) (2022)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Continual Learning on Dynamic Graphs via Parameter Isolation](https://mlsanity.com/paper/2305.13825/) (2023)
- [Towards Fair Graph Neural Networks via Graph Counterfactual](https://mlsanity.com/paper/2307.04937/) (2023)
- [Test-Time Training for Graph Neural Networks](https://mlsanity.com/paper/2210.08813/) (2022)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Structure Guided Multi-modal Pre-trained Transformer for Knowledge Graph Reasoning](https://mlsanity.com/paper/2307.03591/) (2023)
- [SpherE: Expressive and Interpretable Knowledge Graph Embedding for Set Retrieval](https://mlsanity.com/paper/2404.19130/) (2024)
- [Towards Enhancing Relational Rules for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2310.13411/) (2023)
- [Enhancing Large Language Model for Knowledge Graph Completion via Structure-Aware Alignment-Tuning](https://mlsanity.com/paper/2509.01166/) (2025)
- [RAPO: An Adaptive Ranking Paradigm for Bilingual Lexicon Induction](https://mlsanity.com/paper/2210.09926/) (2022)
- [MQuinE: a cure for "Z-paradox" in knowledge graph embedding models](https://mlsanity.com/paper/2402.03583/) (2024)
- [STAGE: Simplified Text-Attributed Graph Embeddings Using Pre-trained LLMs](https://mlsanity.com/paper/2407.12860/) (2024)
- [Bridging External and Parametric Knowledge: Mitigating Hallucination of LLMs with Shared-Private Semantic Synergy in Dual-Stream Knowledge](https://mlsanity.com/paper/2506.06240/) (2025)
- [To Copy Rather Than Memorize: A Vertical Learning Paradigm for Knowledge Graph Completion](https://mlsanity.com/paper/2305.14126/) (2023)
- [Relation-aware Ensemble Learning for Knowledge Graph Embedding](https://mlsanity.com/paper/2310.08917/) (2023)
- [HyperMono: A Monotonicity-aware Approach to Hyper-Relational Knowledge Representation](https://mlsanity.com/paper/2404.09848/) (2024)
- [Efficient Learning on Large Graphs using a Densifying Regularity Lemma](https://mlsanity.com/paper/2504.18273/) (2025)
- [DuetGraph: Coarse-to-Fine Knowledge Graph Reasoning with Dual-Pathway Global-Local Fusion](https://mlsanity.com/paper/2507.11229/) (2025)
- [Improving Enzyme Prediction with Chemical Reaction Equations by Hypergraph-Enhanced Knowledge Graph Embeddings](https://mlsanity.com/paper/2601.05330/) (2026)
- [Learning Complete Topology-Aware Correlations Between Relations for Inductive Link Prediction](https://mlsanity.com/paper/2309.11528/) (2023)
- [Node-based Knowledge Graph Contrastive Learning for Medical Relationship Prediction](https://mlsanity.com/paper/2310.10138/) (2023)
- [CL4KGE: A Curriculum Learning Method for Knowledge Graph Embedding](https://mlsanity.com/paper/2408.14840/) (2024)
- [Efficient Relational Context Perception for Knowledge Graph Completion](https://mlsanity.com/paper/2501.00397/) (2024)
- [MPRM: A Markov Path-based Rule Miner for Efficient and Interpretable Knowledge Graph Reasoning](https://mlsanity.com/paper/2505.12329/) (2025)
- [Relations Are Channels: Knowledge Graph Embedding via Kraus Decompositions](https://mlsanity.com/paper/2605.10317/) (2026)
- [Q-GNN: Query-Conditioned Graph Neural Networks with Type Awareness for Knowledge Graph Completion](https://mlsanity.com/paper/2606.05639/) (2026)
- [Generalized Rank-based Evaluation for Knowledge Graph Completion: Perspectives, Framework, and Analyses](https://mlsanity.com/paper/2606.08921/) (2026)

## Abstract (arXiv)

The effectiveness of knowledge graph embedding (KGE) largely depends on the ability to model intrinsic relation patterns and mapping properties. However, existing approaches can only capture some of them with insufficient modeling capacity. In this work, we propose a more powerful KGE framework named HousE, which involves a novel parameterization based on two kinds of Householder transformations: (1) Householder rotations to achieve superior capacity of modeling relation patterns; (2) Householder projections to handle sophisticated relation mapping properties. Theoretically, HousE is capable of modeling crucial relation patterns and mapping properties simultaneously. Besides, HousE is a generalization of existing rotation-based models while extending the rotations to high-dimensional spaces. Empirically, HousE achieves new state-of-the-art performance on five benchmark datasets. Our code is available at https://github.com/anrep/HousE.