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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.
• 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.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.