Stable vectorization of multiparameter persistent homology using signed barcodes as measures
Persistent homology (PH) provides topological descriptors for geometric data, such as
weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …
weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …
On the expressivity of persistent homology in graph learning
R Ballester, B Rieck - arXiv preprint arXiv:2302.09826, 2023 - arxiv.org
Persistent homology, a technique from computational topology, has recently shown strong
empirical performance in the context of graph classification. Being able to capture long …
empirical performance in the context of graph classification. Being able to capture long …
On the expressivity of persistent homology in graph learning
R Ballester, B Rieck - The Third Learning on Graphs Conference, 2024 - openreview.net
Persistent homology, a technique from computational topology, has recently shown strong
empirical performance in the context of graph classification. Being able to capture long …
empirical performance in the context of graph classification. Being able to capture long …
Graphcode: Learning from multiparameter persistent homology using graph neural networks
We introduce graphcodes, a novel multi-scale summary of the topological properties of a
dataset that is based on the well-established theory of persistent homology. Graphcodes …
dataset that is based on the well-established theory of persistent homology. Graphcodes …
Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data
H Wagner - 39th International Symposium on Computational …, 2023 - drops.dagstuhl.de
We focus on efficient computations of topological descriptors for voxel data. This type of data
includes 2D greyscale images, 3D medical scans, but also higher-dimensional scalar fields …
includes 2D greyscale images, 3D medical scans, but also higher-dimensional scalar fields …
Curvature sets over persistence diagrams
M Gómez, F Mémoli - Discrete & Computational Geometry, 2024 - Springer
We study a family of invariants of compact metric spaces that combines the Curvature Sets
defined by Gromov in the 1980 s with Vietoris–Rips Persistent Homology. For given integers …
defined by Gromov in the 1980 s with Vietoris–Rips Persistent Homology. For given integers …
Cup product persistence and its efficient computation
It is well-known that cohomology has a richer structure than homology. However, so far, in
practice, the use of cohomology in persistence setting has been limited to speeding up of …
practice, the use of cohomology in persistence setting has been limited to speeding up of …
Topological Delaunay Graph for Efficient 3D Binary Image Analysis
Topological data analysis (TDA) based on persistent homology (PH) has become
increasingly popular in automation technology. Recent advances in imaging and simulation …
increasingly popular in automation technology. Recent advances in imaging and simulation …
Computational methods for multi-parameter persistence
F Lenzen - 2023 - mediatum.ub.tum.de
In the past, persistent cohomology was a major ingredient in improving the efficiency of
persistent homology. However, persistent cohomology has not been successfully applied in …
persistent homology. However, persistent cohomology has not been successfully applied in …
New Invariants and Algorithms for Persistence over Posets
N Clause - 2024 - search.proquest.com
Persistent homology is a central tool in topological data analysis that allows us to study the
shape of data. In the one-parameter setting, there is a lossless, discrete representation of the …
shape of data. In the one-parameter setting, there is a lossless, discrete representation of the …