Topology-Inspired Clustering Hierarchy for Graph Autoencoders via Spectral Graph Theory

The present study introduces a normalized eigengap heuristic to automatically generate a topology-inspired clustering hierarchy of an unstructured mesh by leveraging spectral clustering. The heuristic is particularly useful for graph autoencoders that leverage a clustering hierarchy to encode graph-structured data into a low-dimensional representation. In the previous work of the authors on a hierarchical graph autoencoder, the number of nodes in the clustering hierarchy was a user-defined hyperparameter. In this study, a normalized eigengap heuristic is proposed to define the number of nodes at each layer in the clustering hierarchy. Furthermore, two different schemes are presented for generating the clustering hierarchy. The normalized eigengap heuristic is assessed on two benchmark cases for a 2D unstructured mesh with inherent clustered topology, and it is demonstrated that the normalized eigengap heuristic accurately identifies the anticipated optimal number of nodes and their corresponding clusters.