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Benchmarking R packages for Calculation of Persistent Homology
Eashwar V Somasundaram1, Shael E Brown2, Adam Litzler3
1School of Medicine, Case Western Reserve University, Cleveland, OH 44106, United States.
The R Journal
|September 13, 2021
Summary
We benchmarked R packages for persistent homology analysis. GUDHI in TDA is fastest for low dimensions, while Ripser in TDAstats excels for high dimensions and memory efficiency.
Area of Science:
- Topological Data Analysis (TDA)
- Computational Topology
- Data Science Software
Background:
- Persistent homology is a key tool in TDA for analyzing shape and structure in data.
- Several R packages (TDA, TDAstats) wrap powerful underlying libraries (Dionysus, GUDHI, Ripser).
- These TDA tools are computationally intensive and lack formal performance benchmarks.
Purpose of the Study:
- To formally benchmark the runtime and memory usage of R packages for persistent homology.
- To compare the performance of TDA and TDAstats packages and their underlying libraries: Dionysus, GUDHI, and Ripser.
- To identify the most efficient software for persistent homology calculations across different dataset dimensions.
Main Methods:
- Benchmarking of runtime and memory consumption for TDA and TDAstats R packages.
- Evaluation of underlying libraries: Dionysus, GUDHI, and Ripser.
- Analysis across varying dataset dimensions to assess scalability.
Main Results:
- For datasets with fewer than 3 dimensions, the GUDHI library within the TDA package offers the fastest computation.
- For higher-dimensional datasets, the Ripser library, accessed via the TDAstats package, demonstrates superior speed.
- Ripser and TDAstats are identified as the most memory-efficient options for persistent homology calculations.
Conclusions:
- The choice of persistent homology software in R depends on dataset dimensionality.
- GUDHI (in TDA) is recommended for low-dimensional data, while Ripser (in TDAstats) is optimal for high-dimensional data.
- Ripser and TDAstats provide the best memory efficiency for persistent homology analysis.
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