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TDAstats - Pipeline for Topological Data Analysis

A comprehensive toolset for any useR conducting topological data analysis, specifically via the calculation of persistent homology in a Vietoris-Rips complex. The tools this package currently provides can be conveniently split into three main sections: (1) calculating persistent homology; (2) conducting statistical inference on persistent homology calculations; (3) visualizing persistent homology and statistical inference. The published form of TDAstats can be found in Wadhwa et al. (2018) <doi:10.21105/joss.00860>. For a general background on computing persistent homology for topological data analysis, see Otter et al. (2017) <doi:10.1140/epjds/s13688-017-0109-5>. To learn more about how the permutation test is used for nonparametric statistical inference in topological data analysis, read Robinson & Turner (2017) <doi:10.1007/s41468-017-0008-7>. To learn more about how TDAstats calculates persistent homology, you can visit the GitHub repository for Ripser, the software that works behind the scenes at <https://github.com/Ripser/ripser>. This package has been published as Wadhwa et al. (2018) <doi:10.21105/joss.00860>.

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data-scienceggplot2homologyhomology-calculationshomology-computationjosspersistent-homologypipelineripsertdatopological-data-analysistopologytopology-visualizationvisualizationcpp

8.79 score 41 stars 2 dependents 70 scripts 373 downloads

ripserr - Calculate Persistent Homology with Ripser-Based Engines

Ports the Ripser <doi:10.48550/arXiv.1908.02518> and Cubical Ripser <doi:10.48550/arXiv.2005.12692> persistent homology calculation engines from C++. Can be used as a rapid calculation tool in topological data analysis pipelines.

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algebraic-topologycohomologycppcubical-complexpersistent-homologypixelpoint-cloudr-languager-programmingrcpprips-complexripsersimplicial-complexsimplicial-homologytopological-data-analysistopologyvietoris-complexvoxelcpp

7.41 score 12 stars 51 scripts 217 downloads

phutil - Persistence Homology Utilities

A low-level package for hosting persistence data. It is part of the 'TDAverse' suite of packages, which is designed to provide a collection of packages for enabling machine learning and data science tasks using persistent homology. Implements a class for hosting persistence data, a number of coercers from and to already existing and used data structures from other packages and functions to compute distances between persistence diagrams. A formal definition and study of bottleneck and Wasserstein distances can be found in Bubenik, Scott and Stanley (2023) <doi:10.1007/s41468-022-00103-8>. Their implementation in 'phutil' relies on the 'C++' Hera library developed by Kerber, Morozov and Nigmetov (2017) <doi:10.1145/3064175>.

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quartocppopenmp

6.16 score 2 dependents 30 scripts 582 downloads

tdaunif - Uniform Manifold Samplers for Topological Data Analysis

Uniform random samples from simple manifolds, sometimes with noise, are commonly used to test topological data analytic (TDA) tools. This package includes samplers powered by two techniques: analytic volume-preserving parameterizations, as employed by Arvo (1995) <doi:10.1145/218380.218500>, and rejection sampling, as employed by Diaconis, Holmes, and Shahshahani (2013) <doi:10.1214/12-IMSCOLL1006>.

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manifoldssamplertdatopological-data-analysistopological-statistics

4.86 score 4 stars 12 scripts 143 downloads

tdarec - A 'recipes' Extension for Persistent Homology and Its Vectorizations

Topological data analytic methods in machine learning rely on vectorizations of the persistence diagrams that encode persistent homology, as surveyed by Ali &al (2000) <doi:10.48550/arXiv.2212.09703>. Persistent homology can be computed using 'TDA' and 'ripserr' and vectorized using 'TDAvec'. The Tidymodels package collection modularizes machine learning in R for straightforward extensibility; see Kuhn & Silge (2022, ISBN:978-1-4920-9644-3). These 'recipe' steps and 'dials' tuners make efficient algorithms for computing and vectorizing persistence diagrams available for Tidymodels workflows.

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machine-learningpersistent-homologyrecipestidymodelstopological-data-analysisvectorization

4.77 score 1 stars 17 scripts 499 downloads

inphr - Statistical Inference for Persistence Homology Data

A set of functions for performing null hypothesis testing on samples of persistence diagrams using the theory of permutations. Currently, only two-sample testing is implemented. Inputs can be either samples of persistence diagrams themselves or vectorizations. In the former case, they are embedded in a metric space using either the Bottleneck or Wasserstein distance. In the former case, persistence data becomes functional data and inference is performed using tools available in the 'fdatest' package. Main reference for the interval-wise testing method: Pini A., Vantini S. (2017) "Interval-wise testing for functional data" <doi:10.1080/10485252.2017.1306627>. Main reference for inference on populations of networks: Lovato, I., Pini, A., Stamm, A., & Vantini, S. (2020) "Model-free two-sample test for network-valued data" <doi:10.1016/j.csda.2019.106896>.

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3.18 score 1 stars 7 scripts 179 downloads