Benchmarking R packages for Calculation of Persistent Homology.

Shael,E. Brown,Eashwar,V. Somasundaram,Jacob,G. Scott,Raoul,R. Wadhwa,Adam Litzler

doi:10.32614/rj-2021-033

Abstract

Several persistent homology software libraries have been implemented in R. Specifically, the Dionysus, GUDHI, and Ripser libraries have been wrapped by the TDA and TDAstats CRAN packages. These software represent powerful analysis tools that are computationally expensive and, to our knowledge, have not been formally benchmarked. Here, we analyze runtime and memory growth for the 2 R packages and the 3 underlying libraries. We find that datasets with less than 3 dimensions can be evaluated with persistent homology fastest by the GUDHI library in the TDA package. For higher-dimensional datasets, the Ripser library in the TDAstats package is the fastest. Ripser and TDAstats are also the most memory-efficient tools to calculate persistent homology.

Highlights

Topological data analysis (TDA) is a broad set of methodologies that characterizes structural features of datasets inspired by topological principles
We focus on persistent homology of the Vietoris-Rips and alpha complexes, which use simplicial complexes to approximate topologic relationships in point clouds
There are several different methods to construct a simplicial complex on a given point cloud S, but this paper focuses on the Vietoris-Rips and alpha complexes

Summary

Introduction

Topological data analysis (TDA) is a broad set of methodologies that characterizes structural features of datasets inspired by topological principles. It has a broad range of usage, from viral evolution to physical chemistry (Chan et al, 2013; Offroy and Duponchel, 2016). In the basic workflow of persistent homology, a series of simplicial complexes are generated on point clouds to characterize topological features. We measure features that are discovered by the algorithm at a particular stage and disappear at a later stage. The difference between these stages is persistence. Features with larger persistence more likely represent real geometric patterns rather than noise

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