GLEE: Geometric Laplacian Eigenmap Embedding
This work addresses graph embedding for downstream tasks, offering a novel geometric perspective that improves performance over existing methods.
The paper tackles the problem of graph embedding by proposing a new approach, GLEE, which uses geometric properties from the Laplacian matrix instead of traditional distance-minimization, and demonstrates that it outperforms other techniques in graph reconstruction and link prediction.
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.