Global graph features unveiled by unsupervised geometric deep learning
This addresses the problem of graph analysis for researchers in fields like neuroscience and physics, offering a novel method for disentangling invariant features from noise, though it is incremental as it builds on existing geometric deep learning techniques.
The paper tackled the challenge of analyzing and classifying graphs with structural variability by introducing GAUDI, an unsupervised geometric deep learning framework that captures local and global features, resulting in consistent mapping of similar graphs into nearby latent regions and demonstrating superior performance across applications like brain connectivity analysis.
Graphs provide a powerful framework for modeling complex systems, but their structural variability poses significant challenges for analysis and classification. To address these challenges, we introduce GAUDI (Graph Autoencoder Uncovering Descriptive Information), a novel unsupervised geometric deep learning framework designed to capture both local details and global structure. GAUDI employs an innovative hourglass architecture with hierarchical pooling and upsampling layers linked through skip connections, which preserve essential connectivity information throughout the encoding-decoding process. Even though identical or highly similar underlying parameters describing a system's state can lead to significant variability in graph realizations, GAUDI consistently maps them into nearby regions of a structured and continuous latent space, effectively disentangling invariant process-level features from stochastic noise. We demonstrate GAUDI's versatility across multiple applications, including small-world networks modeling, characterization of protein assemblies from super-resolution microscopy, analysis of collective motion in the Vicsek model, and identification of age-related changes in brain connectivity. Comparison with related approaches highlights GAUDI's superior performance in analyzing complex graphs, providing new insights into emergent phenomena across diverse scientific domains.