The Deep Latent Position Block Model for Block Clustering and Latent Representation of Nodes in Networks

The current surge in data has led to a significant increase in the size of networks used to model relationships between different objects represented as nodes. Therefore, summarising network information is a crucial task that can be conducted using node clustering methods. Additionally, to ensure interpretable results, it is essential to employ relevant visualisation techniques to depict the network. To tackle both issues, we propose a new methodology called the deep latent position block model (Deep LPBM). This simultaneously provides a network visualisation coherent with block modelling, allowing a clustering more general than community detection methods, as well as a continuous representation of nodes in a latent space given by partial membership vectors. Deep LPBM is based on a variational autoencoder strategy, relying on a graph convolutional network, with a specifically designed decoder. The inference involves the construction of an approximation of the marginal likelihood of Deep LPBM through the expected lower bound (ELBO). A gradient-descent algorithm based on Monte-Carlo approximations is used to optimize the ELBO with respect to its parameters. To select the number of clusters, we compare three model selection criteria. A node clustering benchmark comprising positional community detection as well as model methods is conducted. We also compare the quality of Deep LPBM node partial membership estimation with other methodologies. We conclude with an analysis of the French political blogosphere network and a comparison with another methodology to illustrate the novelty provided by Deep LPBM results.