Neural Network-Based Approach

Deep autoencoders

Neural network methods like deep autoencoders generate graph embeddings using an encoder-decoder model. A few of the embedding algorithms that use neural networks are listed below.

Structural deep network embedding (SDNE)

This algorithm tries to preserve the first- and second-order proximities. The first-order proximity defines the pairwise proximity of the nodes—that is, a first-order proximity exists between node u and node v if a link exists between them. The second-order proximity between two nodes means there is neighborhood network similarity.

Let Nu be a list of all first-order proximities of the node u with all other nodes. Then, the similarity between Nu and Nv is called second-order proximity. A mapping function is learned to capture the similarities between the embeddings of node u and node v so that the first and second-order proximities of both nodes can be preserved.

SDNE uses a semi-supervised model (unsupervised + supervised models) to tackle the case of both proximities. The unsupervised model in the SDNE is an autoencoder that learns the embeddings. The supervised part is based on Laplacian Eigenmaps, which set penalties if similar nodes are mapped away from each other in the embedding space.