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)
Topological Data Analysis: Simplicial Complex
SimplicialComplex is a user-friendly Topological Data Analysis (TDA) package written entirely in R. While most TDA libraries (Dionysus, PHAT, GUDHI) are developed in Python and C++, implementing simplicial complexes natively in R makes them directly compatible with the rich ecosystem of statistical methods R already offers.
Features
- Simplicial complexes: Build Vietoris–Rips, Alpha, Cech, Witness, Cubical, and Flood complexes from point clouds, or define abstract simplicial complexes by hand.
- Topological invariants: Faces, boundary matrices, Betti numbers, and the Euler characteristic.
- Persistent homology: filtrations, boundary-matrix reduction, persistence pairs, persistence diagrams, and persistence landscape.
- Statistical: Wasserstein distance & bottleneck distance were built in the latest version, with matching plot.
- Time/Step consideration: CROCKER and Zigzag persistence with plots.
- Discrete Morse Theory: Discrete Morse Vector Fields (DMVF) with plots.
- Laplacians: Basic Laplacian, persistent laplacian, and hodge laplacian
- Examples: Full worked examples in
inst/example.
Playground
Try the interactive playground to get familiar with all the concepts used in TDA.
References
- Zomorodian, A., & Carlsson, G. (2004). Computing persistent homology. Proceedings of the Twentieth Annual Symposium on Computational Geometry, 347–356.
- Chazal, F., & Michel, B. (2021). An introduction to topological data analysis: Fundamental and practical aspects for data scientists. Frontiers in Artificial Intelligence, 4, 667963.
- Graf, F., Pellizzoni, P., Uray, M., Huber, S., & Kwitt, R. (2025). The Flood Complex: Large-scale persistent homology on millions of points. Advances in Neural Information Processing Systems, 38.
- Otter, N., Porter, M. A., Tillmann, U., Grindrod, P., & Harrington, H. A. (2017). A roadmap for the computation of persistent homology. EPJ data science, 6(1), 17.
- Wei, X., & Wei, G. W. (2025). Persistent topological laplacians—a survey. Mathematics, 13(2), 208.
- Dey, T. K., & Wang, Y. (1945). Computational topology for data analysis. American history, 1861(1900).