Hodge Laplacian

The Hodge Laplacian is a mathematical operator extending the graph Laplacian to higher-dimensional data structures like simplicial complexes, enabling analysis of data with complex topological features. Current research focuses on applying the Hodge Laplacian within machine learning frameworks, particularly graph neural networks, developing algorithms like persistent Hodge Laplacian learning and Hodge-Laplacian-based heterogeneous graph attention networks to analyze data on manifolds and complex graphs. This work has significant implications for various fields, improving the analysis of volumetric data (e.g., in biomedicine) and enhancing the performance of graph-based machine learning models across diverse applications, including those in computer vision, neuroscience, and chemistry.