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>.
