Introduction to the R package TDA

TL;DR

The paper introduces the R package TDA, which offers tools for topological data analysis, including functions for computing topological features of data and integrating efficient algorithms for persistent homology.

Contribution

It provides a comprehensive R interface to topological data analysis tools, including persistent homology computations and density clustering algorithms, with integration of C++ libraries.

Findings

Provides functions for topological feature extraction from data.

Includes algorithms for density clustering and visualization.

Integrates efficient C++ libraries for persistent homology.

Abstract

We present a short tutorial and introduction to using the R package TDA, which 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 recently developed statistical methods. 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.