# Graph Spectral Embedding using the Geodesic Betweeness Centrality

arXiv: https://arxiv.org/abs/2205.03544 · HTML: https://mlsanity.com/paper/2205.03544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 7 May 2022.

## Builds on (most cited first, 6 of 6)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets](https://mlsanity.com/paper/2110.12752/) (2021)
- [Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths](https://mlsanity.com/paper/1410.6572/) (2014)
- [Zero Shot Learning with the Isoperimetric Loss](https://mlsanity.com/paper/1903.06781/) (2019)

## Abstract (arXiv)

We introduce the Graph Sylvester Embedding (GSE), an unsupervised graph representation of local similarity, connectivity, and global structure. GSE uses the solution of the Sylvester equation to capture both network structure and neighborhood proximity in a single representation. Unlike embeddings based on the eigenvectors of the Laplacian, GSE incorporates two or more basis functions, for instance using the Laplacian and the affinity matrix. Such basis functions are constructed not from the original graph, but from one whose weights measure the centrality of an edge (the fraction of the number of shortest paths that pass through that edge) in the original graph. This allows more flexibility and control to represent complex network structure and shows significant improvements over the state of the art when used for data analysis tasks such as predicting failed edges in material science and network alignment in the human-SARS CoV-2 protein-protein interactome.