Embedding graphs with Laplacian Eigenmaps

Graph laplacian eigenmaps (GLE) are one means, among many, of embedding graphs into a low-dimensional numeric space. Specifically, GLE is an approach based on Matrix Factorization that takes as input non-relational data and outputs node embeddings. The key insight of GLEs is that the graph property to be preserved can be interpreted as pairwise node similarities. Thus, a larger penalty is imposed if two nodes with large similarity are embedded far apart.