# Pseudo-Euclidean Attract-Repel Embeddings for Undirected Graphs

arXiv: https://arxiv.org/abs/2106.09671 · HTML: https://mlsanity.com/paper/2106.09671/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [PyTorch-BigGraph: A Large-scale Graph Embedding System](https://mlsanity.com/paper/1903.12287/) (2019)
- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [Generating Personalized Recipes from Historical User Preferences](https://mlsanity.com/paper/1909.00105/) (2019)
- [The impossibility of low rank representations for triangle-rich complex networks](https://mlsanity.com/paper/2003.12635/) (2020)
- [Node Embeddings and Exact Low-Rank Representations of Complex Networks](https://mlsanity.com/paper/2006.05592/) (2020)
- [SHOPPER: A Probabilistic Model of Consumer Choice with Substitutes and Complements](https://mlsanity.com/paper/1711.03560/) (2017)
- [Exponential Family Embeddings](https://mlsanity.com/paper/1608.00778/) (2016)
- [Directed Graph Embeddings in Pseudo-Riemannian Manifolds](https://mlsanity.com/paper/2106.08678/) (2021)

## Built on by (most cited first, 1 of 1)

- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)

## Abstract (arXiv)

Dot product embeddings take a graph and construct vectors for nodes such that dot products between two vectors give the strength of the edge. Dot products make a strong transitivity assumption, however, many important forces generating graphs in the real world lead to non-transitive relationships. We remove the transitivity assumption by embedding nodes into a pseudo-Euclidean space - giving each node an attract and a repel vector. The inner product between two nodes is defined by taking the dot product in attract vectors and subtracting the dot product in repel vectors. Pseudo-Euclidean embeddings can compress networks efficiently, allow for multiple notions of nearest neighbors each with their own interpretation, and can be `slotted' into existing models such as exponential family embeddings or graph neural networks for better link prediction.