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Persistent homology (Edelsbrunner & Harer, 2008) is a relatively recent computational technique that extracts topological information from various kinds of datasets. This topological information gives us a good overview of the global shape of the data as well as giving us a description of its local geometry. Since its introduction, it has been used in a diverse range of applications, including biology (Bernoff & Topaz, 2016), material science (Lee et al., 2017), signal processing (Tralie, 2016), and computer vision (Asaad & Jassim, 2017). A problem persistent homology faces is the very large size of combinatorial structures it has to work with. Recent algorithmic advances employ various computational shortcuts to overcome this problem.

Ripserer.jl: flexible and efficient persistent homology computation in Julia