# From One Point to A Manifold: Knowledge Graph Embedding For Precise Link Prediction

arXiv: https://arxiv.org/abs/1512.04792 · HTML: https://mlsanity.com/paper/1512.04792/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2015.

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

- [Differentially Private Federated Knowledge Graphs Embedding](https://mlsanity.com/paper/2105.07615/) (2021)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [A Benchmark and Comprehensive Survey on Knowledge Graph Entity Alignment via Representation Learning](https://mlsanity.com/paper/2103.15059/) (2021)
- [UUKG: Unified Urban Knowledge Graph Dataset for Urban Spatiotemporal Prediction](https://mlsanity.com/paper/2306.11443/) (2023)
- [Normalizing Flow-based Neural Process for Few-Shot Knowledge Graph Completion](https://mlsanity.com/paper/2304.08183/) (2023)
- [Geometry Interaction Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.12418/) (2022)
- [KRACL: Contrastive Learning with Graph Context Modeling for Sparse Knowledge Graph Completion](https://mlsanity.com/paper/2208.07622/) (2022)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Negative Sampling in Knowledge Graph Representation Learning: A Review](https://mlsanity.com/paper/2402.19195/) (2024)
- [TranSHER: Translating Knowledge Graph Embedding with Hyper-Ellipsoidal Restriction](https://mlsanity.com/paper/2204.13221/) (2022)
- [Quant 4.0: Engineering Quantitative Investment with Automated, Explainable and Knowledge-driven Artificial Intelligence](https://mlsanity.com/paper/2301.04020/) (2022)
- [FMGNN: Fused Manifold Graph Neural Network](https://mlsanity.com/paper/2304.01081/) (2023)
- [Building A Knowledge Graph to Enrich ChatGPT Responses in Manufacturing Service Discovery](https://mlsanity.com/paper/2404.06571/) (2024)
- [Knowledge Graph Embeddings: A Comprehensive Survey on Capturing Relation Properties](https://mlsanity.com/paper/2410.14733/) (2024)
- [Knowledge Graph Embedding by Normalizing Flows](https://mlsanity.com/paper/2409.19977/) (2024)
- [Knowledgebra: An Algebraic Learning Framework for Knowledge Graph](https://mlsanity.com/paper/2204.07328/) (2022)
- [ProjB: An Improved Bilinear Biased ProjE model for Knowledge Graph Completion](https://mlsanity.com/paper/2209.02390/) (2022)
- [Post-hoc and manifold explanations analysis of facial expression data based on deep learning](https://mlsanity.com/paper/2404.18352/) (2024)
- [Logical Expressivity and Explanations for Monotonic GNNs with Scoring Functions](https://mlsanity.com/paper/2508.14091/) (2025)

## Abstract (arXiv)

Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space. However, existing methods could not characterize the knowledge graph in a fine degree to make a precise prediction. There are two reasons: being an ill-posed algebraic system and applying an overstrict geometric form. As precise prediction is critical, we propose an manifold-based embedding principle (ManifoldE) which could be treated as a well-posed algebraic system that expands the position of golden triples from one point in current models to a manifold in ours. Extensive experiments show that the proposed models achieve substantial improvements against the state-of-the-art baselines especially for the precise prediction task, and yet maintain high efficiency.