Flexible and efficient persistent homology computation.
Author: Matija Čufar (@mtsch)
Introduction
Ripserer is a pure Julia library for computing persistent homology based on the Ripser algorithm. Roughly speaking, persistent homology detects the global topological and local geometric structure of data in a noise-resistant, stable way. If you are unfamiliar with persistent homology, I recommend reading this excellent introduction.
Please see the Usage Guide for a quick introduction, and the API page for detailed descriptions of Ripserer's functionality.
While this package is fully functional, it is still in development and should not be considered stable. I try to disrupt the public interface as little as possible, but breaking changes might still occur from time to time.
Installation
This package is registered. To install it, simply run the following and everything should just work.
julia> import Pkg
julia> Pkg.add("Ripserer")All versions of Julia from 1.0 onward are supported, but I recommend using the latest version of Julia for optimal performance.
Features
Ripserer and its companion package PersistenceDiagrams.jl currently support
- Fast Vietoris-Rips and cubical, and alpha complex persistent homology computation.
- Representative cocycle, cycle, and critical simplex computation.
- Convenient persistence diagram and representative cocycle visualization via Plots.jl. Experimental Makie.jl is also available here.
- Bottleneck and Wasserstein matching and distance computation.
- Various persistence diagram vectorization functions, implemented with persistence images and persistence curves.
- Easy extensibility through a documented API.
- Integration with MLJ.jl.
- Experimental shortest representative cycle computation.
- Experimental sparse circular coordinate computation.
To access some of the features, you need to use the PersistenceDiagrams.jl package.
Performance
Much like Ripser, Ripserer uses several computational tricks to achieve its speed. Among others, these include an implicit simplicial complex representation and the clearing optimization. For a more detailed overview of these optimizations, check out Ulrich Bauer's article on Ripser.
In general, the performance of Ripserer is very close to Ripser, usually within around 30%. Ripserer's strength performance-wise is very sparse inputs, where it can sometimes outperform Ripser. It also computes some things Ripser skips, like the critical simplices.
Ripserer's Cubical homology is up to 3× slower than that of Cubical Ripser, which uses a more specialized algorithm. Ripserer is still a good choice for small 3d images and large 2d images. Unlike Cubical Ripser, it also supports computations on images of dimensions higher than 4.
See the Benchmarks section for more detailed benchmarks.
Extending
Ripserer is designed to be easily extended with new simplex or filtration types. See the Abstract Types and Interfaces API section for more information.
If you have written an extension or are having trouble implementing one, please feel free to open a pull request or an issue. You may also contact me directly.
Contributing
All contributions are welcome, even small things like typo fixes and ideas! See the contribution guidelines for more information.
If you used this software in a cool project, or if you have any comments, questions, or suggestions, feel free to contact me at matijacufar@gmail.com.
Citing
If you used Ripserer in your work, consider citing the JOSS paper.
A bibtex entry is provided in CITATION.bib.