multipers : Multiparameter Persistence for Machine Learning

Scikit-style PyTorch-autodiff multiparameter persistent homology python library. This library aims to provide easy to use and performant strategies for applied multiparameter topology.
Meant to be integrated in the Gudhi library.

Compiled packages

Source	Version	Downloads	Platforms

Quick start

This library allows computing several representations from "geometrical datasets", e.g., point clouds, images, graphs, that have multiple scales. We provide some nice pictures in the documentation. A non-exhaustive list of features can be found in the Features section.

This library is available on pip and conda-forge for (reasonably up to date) Linux, macOS and Windows, via

pip install multipers

or

conda install multipers -c conda-forge

Pre-releases are available via

pip install --pre multipers

These releases typically include minor bug fixes or unstable new features.

Windows support is experimental, and some core dependencies are not available on Windows. We hence recommend Windows user to use WSL.
Documentation and build instructions are available here.

Features, and linked projects

This library features a bunch of different functions and helpers. See below for a non-exhaustive list.
Filled box refers to implemented or interfaced code.

• [Multiparameter Module Approximation, JACT] provides the multiparameter simplicial structure, as well as technics for approximating modules, via interval-decomposable modules. It is also very useful for visualization.
• [Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures, NeurIPS2023] provides fast representations of multiparameter persistence modules, by using their signed barcodes decompositions encoded into signed measures. Implemented decompositions : Euler surfaces, Hilbert function, rank invariant (i.e. rectangles). It also provides representation technics for Machine Learning, i.e., Sliced Wasserstein kernels, and Vectorizations.
• [A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions, NeurIPS2023] Provides a vectorization framework for interval decomposable modules, for Machine Learning. Currently implemented as an extension of MMA.
• [Differentiability and Optimization of Multiparameter Persistent Homology, ICML2024] An approach to compute a (clarke) gradient for any reasonable multiparameter persistent invariant. Currently, any multipers computation is auto-differentiable using this strategy, provided that the input are pytorch gradient capable tensor.
• [Multiparameter Persistence Landscapes, JMLR] A vectorization technic for multiparameter persistence modules.
• [Filtration-Domination in Bifiltered Graphs, ALENEX2023] Allows for 2-parameter edge collapses for 1-critical clique complexes. Very useful to speed up, e.g., Rips-Codensity bifiltrations.
• [Fast free resolutions of bifiltered chain complexes] One-critical representation of multicritical filtrations, using multi_critical.
• [Chunk Reduction for Multi-Parameter Persistent Homology, SoCG2019] Multi-filtration preprocessing algorithm for homology computations.
• [Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology, JAAG] Minimal presentation of multiparameter persistence modules, using mpfree. Hilbert, Rank Decomposition Signed Measures, and MMA decompositions can be computed using the mpfree backend.
• [Hera] Matching distance between 2-parameter presentations, 1-parameter bottleneck/wasserstein distances.
• [Decomposing Multiparameter Persistence Modules, SoCG2025] Using the AIDA and Persistence-Algebra libraries.
• [Delaunay Bifiltrations of Functions on Point Clouds, SODA2024] Provides an alternative to function rips bifiltrations, using Delaunay complexes. Very good alternative to Rips-Density like bifiltrations.
• [Delaunay Core Bifiltration] Bifiltration for point clouds, taking into account the density. Similar to Rips-Density.
• [Computing the Multicover Bifiltration, SOCG2021] Rhomboid Tiling bifiltration. Equivalent to the multicover bifiltration, using rhomboidtiling.
• [Rivet] Interactive two parameter persistence
• [Kernel Operations on the GPU, with Autodiff, without Memory Overflows, JMLR] Although not linked, at first glance, to persistence in any way, this library allows computing blazingly fast signed measures convolutions (and more!) with custom kernels.
• [Projected distances for multi-parameter persistence modules] Provides a strategy to estimate the convolution distance between multiparameter persistence module using projected barcodes. Implementation is a WIP.
• [Efficient Two-Parameter Persistence Computation via Cohomology, SoCG2023] Minimal presentations for 2-parameter persistence algorithm.

If I missed something, or you want to add something, feel free to open an issue.

Authors

David Loiseaux,
Hannah Schreiber (Persistence backend code),
Luis Scoccola (Möbius inversion in python, degree-rips using persistable and RIVET),
Mathieu Carrière (Sliced Wasserstein),
Odin Hoff Gardå (Delaunay Core bifiltration),
Michael Kerber (mpfree, function_delaunay, multi_critical, multi_chunk backends),
Jan Jendrysiak (Module Decomposition (AIDA), Persistence Algebra).

Licensing

multipers distributions that include the compiled external interfaces are provided under GPL-3.0-or-later.

This is due to linked GPL/LGPL third-party components used by the build, notably AIDA, Persistence-Algebra, function_delaunay, mpfree, multi_critical, and multi_chunk.

See THIRD_PARTY_NOTICES.md for dependency details and pinned revisions used in this workspace.

Citation

Please cite this library and its dependencies (see above) when using it in scientific publications; you can use the following journal bibtex entry

@article{multipers,
  title = {Multipers: {{Multiparameter Persistence}} for {{Machine Learning}}},
  shorttitle = {Multipers},
  author = {Loiseaux, David and Schreiber, Hannah},
  year = {2024},
  month = nov,
  journal = {Journal of Open Source Software},
  volume = {9},
  number = {103},
  pages = {6773},
  issn = {2475-9066},
  doi = {10.21105/joss.06773},
  langid = {english},
}

Contributions

Feel free to contribute, report a bug on a pipeline, or ask for documentation by opening an issue.
In particular, if you have a nice example or application that is not taken care in the documentation (see the ./docs/notebooks/ folder), please contact me to add it there.