Software

R package TDA: Statistical Tools for Topological Data Analysis

• Language: R

• Authors: Brittany Terese Fasy, Jisu KIM, Fabrizio Lecci, Clément Maria, Vincent Rouvreau

• Maintainer: Jisu KIM ( jisuk1 [AT] andrew [DOT] cmu [DOT] edu )

• [ CRAN | Reference Manual | Vignettes | Fabrizio’s page | arXiv | BibTeX ]

The R package TDA provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information about the underlying space, such as the distance function, the distance to a measure, the kNN density estimator, the kernel density estimator, and the kernel distance. The salient topological features of the sublevel sets (or superlevel sets) of these functions can be quantified with persistent homology. We provide an R interface for the efficient algorithms of the C++ libraries GUDHI, Dionysus and PHAT, including a function for the persistent homology of the Rips filtration, and one for the persistent homology of sublevel sets (or superlevel sets) of arbitrary functions evaluated over a grid of points. The significance of the features in the resulting persistence diagrams can be analyzed with functions that implement the methods discussed in (Fasy et al. 2014), (Chazal, Fasy, Lecci, Rinaldo, et al. 2014) and (Chazal, Fasy, Lecci, Michel, et al. 2014). The R package TDA also includes the implementation of an algorithm for density clustering, which allows us to identify the spatial organization of the probability mass associated to a density function and visualize it by means of a dendrogram, the cluster tree.

set.seed(0)

library("TDA")
X <- circleUnif(100)
lim <- rep(c(-1.6, 1.6), 2)
by <- 0.05

Xseq <- seq(lim[1], lim[2], by = by)
Yseq <- seq(lim[3], lim[4], by = by)
Grid <- expand.grid(Xseq, Yseq)

m0 <- 0.1

Diag <- gridDiag(X = X, FUN = dtm, lim = lim,
                 by = by, sublevel = TRUE, library = "Dionysus",
                 printProgress = FALSE, m0 = m0)

B <- 20
alpha <- 0.1
band <- bootstrapBand(X = X, FUN = dtm, Grid = Grid, B = B,
                      parallel = FALSE, alpha = alpha, m0 = m0)

par(mfrow = c(1, 2))
plot(X, pch = 16, cex = 0.5, xlab = "", ylab = "")
plot(Diag[["diagram"]], band = 2 * band[["width"]])

DEnsity BAsed CLustering (DeBaCl)

• Language: Python

• Author: Brian Kent

• [ Documentation | Code | PyPI | Brian’s page | arXiv ]

The package DeBaCl is a Python Toolbox for Interactive Data Analysis with Level Set Trees.