# Joint embedding of structure and features via graph convolutional networks

## TL;DR

This paper introduces AN2VEC, a graph convolutional network-based method that disentangles and captures shared and individual information from node features and network structure, improving understanding of social and biological networks.

## Contribution

It presents a novel multitask GCN Variational Autoencoder that separates feature, structure, and shared information in node embeddings, enhancing interpretability and predictive power.

## Key findings

- Shared information improves embedding performance in correlated networks.
- Embedding captures joint feature-structure information effectively.
- Performance increases with higher feature-structure correlation.

## Abstract

The creation of social ties is largely determined by the entangled effects of people's similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of the emergent network structure. We propose \emph{AN2VEC}, a node embedding method which ultimately aims at disentangling the information shared by the structure of a network and the features of its nodes. Building on the recent developments of Graph Convolutional Networks (GCN), we develop a multitask GCN Variational Autoencoder where different dimensions of the generated embeddings can be dedicated to encoding feature information, network structure, and shared feature-network information. We explore the interaction between these disentangled characters by comparing the embedding reconstruction performance to a baseline case where no shared information is extracted. We use synthetic datasets with different levels of interdependency between feature and network characters and show (i) that shallow embeddings relying on shared information perform better than the corresponding reference with unshared information, (ii) that this performance gap increases with the correlation between network and feature structure, and (iii) that our embedding is able to capture joint information of structure and features. Our method can be relevant for the analysis and prediction of any featured network structure ranging from online social systems to network medicine.