Note that a more detailed tutorial on the R TDA package is available here.

Before we begin, load the TDA package. (If the package is not installed, you can install it using RStudio, or type install.packages("TDA").)


Vietoris-Rips Persistence

The ripsDiag function computes the persistence diagram of a Vietoris-Rips complex. It returns a list containing a diagram object, which can be plotted either as a persistence diagram or as a barcode. The ripsDiag function can use any of the libraries GUDHI, Dionysus, or PHAT.

points1 <- read.csv("~/Dropbox/data/point cloud scripts/points1.csv")
plot(points1, xlab="", ylab="", main="points1")

Diag1 <- ripsDiag(X = points1, maxdimension = 1, maxscale = 4, library="GUDHI", location = FALSE, printProgress = FALSE)
plot(Diag1[["diagram"]], main="persistence diagram from points1")

plot(Diag1[["diagram"]], barcode=TRUE, main="barcode from points1")

Superlevelset Persistence

We first compute a density estimator for the point cloud. We will use the Gaussian Kernel Density Estimator (KDE), computed over a grid of points in the plane. We first set up the grid, then compute the density estimator using the kde function provided by the TDA package. We can also plot the density estimator using the perspective plot function persp. Note that the persp function requires many parameters to set the viewing direction and shading.

Xlim <- c(-3,3)
Ylim <- c(-3,3)
by <- 0.1
Xseq <-seq(Xlim[1], Xlim[2], by=by)
Yseq <-seq(Ylim[1], Ylim[2], by=by)
Grid <- expand.grid(Xseq, Yseq)
points1kde <- kde(X=points1, Grid = Grid, h = 0.3)
persp(Xseq, Yseq, matrix(points1kde, ncol = length(Yseq), nrow = length(Xseq)), xlab = "",ylab = "", zlab = "", theta = -20, phi = 35, ltheta = 50, col = 2, d = 0.5, main="KDE points1")