4 papers · 1 filter
Selecting Interpretable Circular Coordinates from Data
Vincent P. Grande, Marina Meila
Circular coordinates obtained from persistent cohomology reveal loop structure in data, but they usually remain abstract: A detected circle does not tell us which measured angle, p…
Point-Level Topological Representation Learning on Point Clouds
Vincent P. Grande, Michael T. Schaub
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homol…
Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal
Vincent P. Grande, Michael T. Schaub
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 classificat…
Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH
Vincent P. Grande, Michael T. Schaub
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 filtratio…