SimplicialComplex: Topological Data Analysis: Simplicial Complex
Provides an implementation of simplicial complexes for
Topological Data Analysis (TDA). The package includes functions to
compute faces, boundary operators, Betti numbers, Euler characteristic,
and to construct simplicial complexes, including Vietoris-Rips, Cech,
Alpha, Delaunay, Witness, flood, and (via a Freudenthal triangulation)
cubical complexes for grid and image data. It also implements persistent
homology, from building filtrations (via a single build_filtration()
entry point covering all of the above) to computing persistence
diagrams, persistence landscapes, and Wasserstein/bottleneck distances
between diagrams, with the aim of helping readers understand the core
concepts of computational topology.
Methods are based on standard references in persistent homology such as
Zomorodian and Carlsson (2005) <doi:10.1007/s00454-004-1146-y>,
Chazal and Michel (2021) <doi:10.3389/frai.2021.667963>, and
Otter, Porter, Tillmann, Grindrod and Harrington (2017)
<doi:10.1140/epjds/s13688-017-0109-5>.
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