TDAstats is an R pipeline for computing persistent homology in topological data analysis.

To install TDAstats, run the following R code:

# install from CRAN
install.packages("TDAstats")

# install development version from GitHub
devtools::install_github("rrrlw/TDAstats")

# install development version with vignettes/tutorials
devtools::install_github("rrrlw/TDAstats", build_vignettes = TRUE)

The following sample code creates two synthetic datasets, and calculates and visualizes their persistent homology to showcase the use of TDAstats.

# load TDAstats
library("TDAstats")

# load sample datasets
data("unif2d")
data("circle2d")

# calculate persistent homology for both datasets
unif.phom <- calculate_homology(unif2d, dim = 1)
circ.phom <- calculate_homology(circle2d, dim = 1)

# visualize first dataset as persistence diagram
plot_persist(unif.phom)

# visualize second dataset as topological barcode
plot_barcode(circ.phom)

A more detailed tutorial can be found in the package vignettes or at this Gist.

TDAstats has 3 primary goals:

1. Calculation of persistent homology: the C++ Ripser project is a lightweight library for calculating persistent homology that outpaces all of its competitors. Given the importance of computational efficiency, TDAstats naturally uses Ripser behind the scenes for homology calculations, using the Rcpp package to integrate the C++ code into an R pipeline (Ripser for R).

2. Statistical inference of persistent homology: persistent homology can be used in hypothesis testing to compare the topological structure of two point clouds. TDAstats uses a permutation test in conjunction with the Wasserstein metric for nonparametric statistical inference.

3. Visualization of persistent homology: persistent homology is visualized using two types of plots - persistence diagrams and topological barcodes. TDAstats provides implementations of both plot types using the ggplot2 framework. Having ggplot2 underlying the plots confers many advantages to the user, including generation of publication-quality plots and customization using the ggplot object returned by TDAstats.

To contribute to TDAstats, you can create issues for any bugs/suggestions on the issues page. You can also fork the TDAstats repository and create pull requests to add features you think will be useful for users.

If you use TDAstats, please consider citing the following (based on use):

• General use of TDAstats: Wadhwa RR, Williamson DFK, Dhawan A, Scott JG. TDAstats: R pipeline for computing persistent homology in topological data analysis. Journal of Open Source Software. 2018; 3(28): 860. doi: 10.21105/joss.00860
• TDAstats to calculate persistent homology (Ripser): Bauer U. Ripser: Efficient computation of Vietoris-Rips persistence barcodes. 2019; arXiv: 1908.02518.
• TDAstats to perform statistical test: Robinson A, Turner K. Hypothesis testing for topological data analysis. J Appl Comput Topol. 2017; 1: 241.

• Brochard A, Blaszczyszyn B, Mallat S, Zhang S. Particle gradient descent model for point process generation. 2020. arXiv:2010.14928. Link to preprint.
• Nguyen DQN, Xing L, Lin L. Community detection, pattern recognition, and hypergraph-based learning: approches using metric geometry and persistent homology. 2020. arXiv:2010.00435. Link to preprint.
• Pinto GVF. Motivic constructions on graphs and networks with stability results. Doctoral Thesis: Universidade Estadual Paulista Rio Claro & Ohio State University. 2020. Link to thesis.
• Gommel M. A Machine Learning Exploration of Topological Data Analysis Applied to Low and High Dimensional fMRI Data. Doctoral Thesis: University of Iowa. 2019. doi: 10.17077/etd.005247. Link to thesis.
• Mémoli F, Singhal K. A Primer on Persistent Homology of Finite Metric Spaces. Bulletin of Mathematical Biology. 2019; 81(7): 2074. Links to paper and preprint
• Srinivasan R, Chander A. Understanding Bias in Datasets using Topological Data Analysis. Fujitsu Laboratories of America. 2019. Link
• Kough D, Neuzil M, Simpson C, Glover R. Analyzing State of the Union Addresses using Topology. University of St. Thomas. 2019. Link
• Rickert J. A Mathematician's Perspective on Topological Data Analysis and R. 2018. Link
• Blog post on Data Management
• Analyzing finance data
• R package for visualizing persistent homology