discrete-heat-kernels-simplicial

Heat kernel smoothing on simplicial complexes applies diffusion across k-simplices using the Hodge Laplacian to denoise higher-order signals. You load your dataset, select a dimension k, and the process regularizes signals beyond standard vertices and edges.

Topological signal processing for higher-order brain networks extends data analysis beyond pairwise connections by representing data as simplicial complexes. It uses Hodge Laplacian diffusion to smooth and analyze signals across these multi-node structures.

Yes, computing the Hodge Laplacian for higher-order network analysis requires a Python environment with numpy, scipy, gudhi, networkx, and nibabel. These dependencies are essential for constructing simplicial complexes and building boundary operators.

To denoise signals on k-simplices rather than just graph vertices, apply discrete heat kernel diffusion over a constructed simplicial complex. This approach leverages boundary operators and the Hodge Laplacian to regularize higher-order topological signals.

Use simplicial complex construction for functional brain connectivity data when you need to model and smooth higher-order interactions beyond standard edges. It enables Hodge Laplacian based diffusion to denoise signals across multi-node structures.

Heat kernel diffusion on the Hodge Laplacian handles sparse computation by utilizing efficient boundary operators. This allows the smoothing process to scale when applying diffusion-based regularization across chosen dimensions of the simplicial complex.