Mirja Granfors, Jesús Pineda, Blanca Zufiria Gerbolés, Daniel Vereb, Joana B. Pereira, Carlo Manzo, and Giovanni Volpe
Learning on graphs and geometry meetup at Uppsala University
Date: 11 February 2025
Place: Uppsala university
Graphs are used to model complex relationships, such as interactions between particles or connections between brain regions. The structural complexity and variability of graphs pose challenges to their efficient analysis and classification. Here, we propose GAUDI (Graph Autoencoder Uncovering Descriptive Information), a graph autoencoder that addresses these challenges. GAUDI’s encoder progressively reduces the size of the graph using multi-step hierarchical pooling, while its decoder incrementally increases the graph size until the original dimensions are restored, focusing on the node and edge features while preserving the graph structure through skip-connections. By training GAUDI to minimize the difference between the node and edge features of the input graph and those of the output graph, it is compelled to capture the most critical parameters describing these features in the latent space, thereby enabling the extraction of essential parameters characterizing the graphs. We demonstrate the performance of GAUDI across diverse graph data originating from complex systems, including the estimation of the parameters of Watts-Strogatz graphs, the classification of protein assembly structures from single-molecule localization microscopy data, the analysis of collective behaviors, and correlations between brain connections and age. This approach offers a robust framework for efficiently analyzing and interpreting complex graph data, facilitating the extraction of meaningful patterns and insights across a wide range of applications.