ripserr: Calculate Persistent Homology of Vietoris-Rips and Cubical Complexes using Ripser in R

Overview

ripserr ports the Ripser and Cubical Ripser persistent homology calculation engines from C++ via Rcpp. It can be used as a convenient and rapid calculation tool in topological data analysis pipelines.

Installation

# install development version
devtools::install_github("rrrlw/ripserr")

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

Sample code

Ripser (Vietoris-Rips complex) can be used as follows for data with dimension greater than or equal to 2.

# load ripserr
library("ripserr")

set.seed(42)
SIZE <- 100

# 2-dimensional example
dataset2 <- rnorm(SIZE * 2)
dim(dataset2) <- c(SIZE, 2)
vr_phom2 <- vietoris_rips(dataset2)
head(vr_phom2)
#>   dimension birth      death
#> 1         0     0 0.01004861
#> 2         0     0 0.02923702
#> 3         0     0 0.04550504
#> 4         0     0 0.06829826
#> 5         0     0 0.06853393
#> 6         0     0 0.07187663
tail(vr_phom2)
#>     dimension     birth     death
#> 112         1 0.3916344 0.4239412
#> 113         1 0.3906770 0.5577989
#> 114         1 0.3880186 0.4029842
#> 115         1 0.3703398 0.5007012
#> 116         1 0.3330234 0.3416054
#> 117         1 0.2418318 0.2504820

# 3-dimensional example
dataset3 <- rnorm(SIZE * 3)
dim(dataset3) <- c(SIZE, 3)
vr_phom3 <- vietoris_rips(dataset3, max_dim = 2) # default: max_dim = 1
head(vr_phom3)
#>   dimension birth     death
#> 1         0     0 0.1282935
#> 2         0     0 0.1421812
#> 3         0     0 0.1516424
#> 4         0     0 0.1819928
#> 5         0     0 0.1858051
#> 6         0     0 0.2114116
tail(vr_phom3)
#>     dimension     birth     death
#> 132         1 0.5212961 0.5233529
#> 133         2 1.1829207 1.1999911
#> 134         2 1.1194325 1.3245908
#> 135         2 1.0707410 1.0914850
#> 136         2 0.9433034 0.9867254
#> 137         2 0.6882204 0.6913078

Cubical Ripser (cubical complex) can be used as follows for data with dimension equal to 2, 3, or 4.

# load ripserr
library("ripserr")

set.seed(42)
SIZE <- 10

# 2-dimensional example
dataset2 <- rnorm(SIZE ^ 2)
dim(dataset2) <- rep(SIZE, 2)
cub_phom2 <- cubical(dataset2)
head(cub_phom2)
#>   dimension      birth      death
#> 1         0 -1.1943289 -0.8607926
#> 2         0 -2.4142076 -0.8509076
#> 3         0 -0.8113932 -0.7844590
#> 4         0 -1.7170087 -0.7844590
#> 5         0 -0.7272921 -0.5428288
#> 6         0 -0.9535234 -0.5428288
tail(cub_phom2)
#>    dimension     birth     death
#> 22         1 0.8217731 0.9333463
#> 23         1 0.7681787 1.0385061
#> 24         1 0.7581632 1.5757275
#> 25         1 0.7208782 1.3025426
#> 26         1 0.6792888 1.4441013
#> 27         1 0.6359504 1.8951935

# 3-dimensional example
dataset3 <- rnorm(SIZE ^ 3)
dim(dataset3) <- rep(SIZE, 3)
cub_phom3 <- cubical(dataset3)
head(cub_phom3)
#>   dimension     birth     death
#> 1         0 -1.926167 -1.737728
#> 2         0 -1.737297 -1.439229
#> 3         0 -1.924950 -1.439229
#> 4         0 -1.500221 -1.354600
#> 5         0 -2.277778 -1.354600
#> 6         0 -1.682481 -1.306676
tail(cub_phom3)
#>     dimension     birth    death
#> 324         2 1.2488637 1.258482
#> 325         2 1.2009654 2.036972
#> 326         2 1.0452759 1.199978
#> 327         2 0.9885968 1.809382
#> 328         2 0.9310749 1.179696
#> 329         2 0.8447922 1.709689

# 4-dimensional example
dataset4 <- rnorm(SIZE ^ 4)
dim(dataset4) <- rep(SIZE, 4)
cub_phom4 <- cubical(dataset4)
head(cub_phom4)
#>   dimension     birth     death
#> 1         0 -1.986299 -1.923519
#> 2         0 -1.822606 -1.816506
#> 3         0 -1.776392 -1.710786
#> 4         0 -1.833663 -1.710387
#> 5         0 -1.947054 -1.704791
#> 6         0 -1.701462 -1.639160
tail(cub_phom4)
#>      dimension    birth    death
#> 4329         3 1.676609 2.019277
#> 4330         3 1.675766 1.932152
#> 4331         3 1.669449 2.149646
#> 4332         3 1.662486 1.863734
#> 4333         3 1.535361 1.963609
#> 4334         3 1.349235 2.263581

Functionality

1. Calculation of persistent homology of Vietoris-Rips complexes using Ripser (function named vietoris_rips).
2. Calculation of persistent homology of cubical complexes using Cubical Ripser (function named cubical).

Citation

If you use the ripserr package in your work, please consider citing the following (based on use):

• General use of ripserr: Wadhwa RR, Piekenbrock M, Scott JG. ripserr: Calculate Persistent Homology with Ripser-based Engines; version 0.1.0. URL https://github.com/rrrlw/ripserr.
• Calculation using Vietoris-Rips complex: Bauer U. Ripser: Efficient computation of Vietoris-Rips persistence barcodes. 2019; arXiv: 1908.02518.
• Calculation using cubical complex: Kaji S, Sudo T, Ahara K. Cubical Ripser: Software for computing persistent homology of image and volume data. 2020; arXiv: 2005.12692.

Contribute

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