A roadmap for the computation of persistent homology
release_t5rot4wzljgazd72us4ozbidxu
by
Nina Otter, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, Heather
A. Harrington
2015
Abstract
Persistent homology (PH) is a method used in topological data analysis (TDA)
to study qualitative features of data that persist across multiple scales. It
is robust to perturbations of input data, independent of dimensions and
coordinates, and provides a compact representation of the qualitative features
of the input. The computation of PH is an open area with numerous important and
fascinating challenges. The field of PH computation is evolving rapidly, and
new algorithms and software implementations are being updated and released at a
rapid pace. The purposes of our article are to (1) introduce theory and
computational methods for PH to a broad range of computational scientists and
(2) provide benchmarks of state-of-the-art implementations for the computation
of PH. We give a friendly introduction to PH, navigate the pipeline for the
computation of PH with an eye towards applications, and use a range of
synthetic and real-world data sets to evaluate currently available open-source
implementations for the computation of PH. Based on our benchmarking, we
indicate which algorithms and implementations are best suited to different
types of data sets. In an accompanying tutorial, we provide guidelines for the
computation of PH. We make publicly available all scripts that we wrote for the
tutorial, and we make available the processed version of the data sets used in
the benchmarking.
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