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Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal
The rich spectral information of the graph Laplacian has been instrumental in graph theory, machine learning, and graph signal processing for applications such as graph classification, clustering, or eigenmode analysis.
Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration.
Topological Point Cloud Clustering
TPCC synthesizes desirable features from spectral clustering and topological data analysis and is based on considering the spectral properties of a simplicial complex associated to the considered point cloud.
Signal Processing on Product Spaces
We establish a framework for signal processing on product spaces of simplicial and cellular complexes.
