# GLEE: Geometric Laplacian Eigenmap Embedding

arXiv: https://arxiv.org/abs/1905.09763 · HTML: https://mlsanity.com/paper/1905.09763/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2019.

## Built on by (most cited first, 2 of 2)

- [GRAPE for Fast and Scalable Graph Processing and random walk-based Embedding](https://mlsanity.com/paper/2110.06196/) (2021)
- [IBB Traffic Graph Data: Benchmarking and Road Traffic Prediction Model](https://mlsanity.com/paper/2408.01016/) (2024)

## Abstract (arXiv)

Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps, which constructs a graph embedding based on the spectral properties of the Laplacian matrix of G. The intuition behind it, and many other embedding techniques, is that the embedding of a graph must respect node similarity: similar nodes must have embeddings that are close to one another. Here, we dispose of this distance-minimization assumption. Instead, we use the Laplacian matrix to find an embedding with geometric properties instead of spectral ones, by leveraging the so-called simplex geometry of G. We introduce a new approach, Geometric Laplacian Eigenmap Embedding (or GLEE for short), and demonstrate that it outperforms various other techniques (including Laplacian Eigenmaps) in the tasks of graph reconstruction and link prediction.