6 citations · 14 across the 8 of their papers we have counts for
9 papers
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…
Don't be Afraid of Cell Complexes! An Introduction from an Applied Perspective
Josef Hoppe, Vincent P. Grande, Michael T. Schaub
Cell complexes (CCs) are a higher-order network model deeply rooted in algebraic topology that has gained interest in signal processing and network science recently. The processing…
Topological Trajectory Classification and Landmark Inference on Simplicial Complexes
Vincent P. Grande, Josef Hoppe, Florian Frantzen +1
We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project th…
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…
ICML 2023 Topological Deep Learning Challenge : Design and Results
Mathilde Papillon, Mustafa Hajij, Helen Jenne +53
This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competi…
Signal Processing on Product Spaces
T. Mitchell Roddenberry, Vincent P. Grande, Florian Frantzen +2
We establish a framework for signal processing on product spaces of simplicial and cellular complexes. For simplicity, we focus on the product of two complexes representing time an…
Topological Point Cloud Clustering
Vincent P. Grande, Michael T. Schaub
We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC sy…