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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
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, and persistence diagrams. Full worked
examples in inst/example.
Flood complex(in development) — a
lightweight filtered complex on landmarks for large-scale persistent
homology, following Graf et al. (NeurIPS 2025).
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.
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.
