GLEE: Geometric Laplacian Eigenmap Embedding

Abstract

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.

References in corpus (8)

• Emergence of scaling in random networks
• DeepWalk: Online Learning of Social Representations
• Cooperative Game Theory Approaches for Network Partitioning
• Graph Embedding Techniques, Applications, and Performance: A Survey
• Hyperbolic Geometry of Complex Networks
• Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec
• Popularity versus Similarity in Growing Networks
• The Simplex Geometry of Graphs

Cited by in corpus (2)

• Neural graph embeddings as explicit low-rank matrix factorization for link prediction
• Zoo Guide to Network Embedding