This repository SIML (Signature Inference & Machine Learning) offers all functionalities and experiments for the paper Persistent Homology as Stopping-Criterion for Voronoi Interpolation. The functions are annotated. The repository is no longer maintained and is used for prototypical implementation of the project. It has been archived since publication. If you use the project, or share this project, please quote us as follows according to DBLP (Natural Neighbor) of DBLP (Voronoi).
@inproceedings{iwcia/MelodiaL20,
author = {Luciano Melodia and
Richard Lenz},
editor = {Tibor Lukic and
Reneta P. Barneva and
Valentin E. Brimkov and
Lidija Comic and
Natasa Sladoje},
title = {Persistent Homology as Stopping-Criterion for Voronoi Interpolation},
booktitle = {Combinatorial Image Analysis - 20th International Workshop, {IWCIA}
2020, Novi Sad, Serbia, July 16-18, 2020, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {12148},
pages = {29--44},
publisher = {Springer},
year = {2020},
url = {https://doi.org/10.1007/978-3-030-51002-2\_3},
doi = {10.1007/978-3-030-51002-2\_3},
}
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tesselation, which induces a natural dual map to the Delaunay triangulation. Advantage is taken from this fact calculating the persistent homology on it after each iteration to capture the changing topology of the data. The boundary points are identified as critical. The Bottleneck and Wasserstein distance serve as a measure of quality between the original point set and the interpolation. If the norm of two distances exceeds a heuristically determined threshold, the algorithm terminates. We give the theoretical basis for this approach and justify its validity with numerical experiments.
For some of the packages written in C++ with corresponding python bindings we use the gcc compiler. Please install gcc using one of the following commands for the linux distributions Arch, Solus4 or Ubuntu:
# Archlinux
sudo pacman -S gcc
# Solus4
sudo eopkg install gcc
# These are the requirements to run gcc for Solus4
sudo eopkg install -c system.devel
# Ubuntu
sudo apt update
sudo apt install build-essential
sudo apt-get install python3-dev
sudo apt-get install manpages-dev
gcc --versionSome packages are way easier to install using Anaconda. For the installation on several linux distributions please follow this link. Further the installation of our clustering prototype requires some python packages to be installed. We provide a requirements file, but here is a complete list for manual installation using pip3 and python 3:
pip3 install pandas
pip3 install sklearn
# Works only with gcc installed.
pip3 install hdbscan
pip3 install gudhi
pip3 install matplotlib
pip3 install tikzplotlib
pip3 install scipy
pip3 install pylab
pip3 install ot
pip3 install typing
pip3 install sklearn
pip3 install csv
pip3 install numpy
# Install Gudhi, easiest installation with Anaconda.
# Gudhi is a library to compute persistent homology.
conda install -c conda-forge gudhi
conda install -c conda-forge/label/cf201901 gudhi- Coricos TDAToolbox, https://github.com/Coricos/TdaToolbox.
- Hirosm: Time Contrastive Learning, https://github.com/hirosm/TCL.
- Indoor WIFI Dataset: UJIIndoorLoc, https://archive.ics.uci.edu/ml/datasets/UJIIndoorLoc.
- Nabihach Tane & CTane, https://github.com/nabihach/FD_CFD_extraction.
- P. Fränti and S. Sieranoja: Clustering Basic Benchmarks, http://cs.joensuu.fi/sipu/datasets/.
- PPoffice: Ant-Colony TSP-Solver, https://github.com/ppoffice/ant-colony-tsp.
- Stwisdom: Optimizers, https://github.com/stwisdom/urnn/blob/master/.
- Submanifolds Neural Persistence, https://github.com/BorgwardtLab/Neural-Persistence.