Topological data analysis studies structure and shape of the data using topological features. We provide a variety of algorithms to learn with persistent homology of the data based on functional summaries for clustering, hypothesis testing, visualization, and others. We refer to Wasserman (2018) <doi:10.1146/annurev-statistics-031017-100045> for a statistical perspective on the topic.

Topological data analysis is a powerful tool for finding non-linear global structure
    in whole datasets. The main tool of topological data analysis is persistent homology, which computes
    a topological shape descriptor of a dataset called a persistence diagram. 'TDApplied' provides 
    useful and efficient methods for analyzing groups of persistence diagrams with machine learning and statistical inference,
    and these functions can also interface with other data science packages to form flexible and integrated
    topological data analysis pipelines.

A comprehensive toolset for any
    useR conducting topological data analysis, specifically via the
    calculation of persistent homology in a Vietoris-Rips complex.
    The tools this package currently provides can be conveniently split
    into three main sections: (1) calculating persistent homology; (2)
    conducting statistical inference on persistent homology calculations;
    (3) visualizing persistent homology and statistical inference.
    The published form of TDAstats can be found in Wadhwa et al. (2018)
    <doi:10.21105/joss.00860>.   
    For a general background on computing persistent homology for
    topological data analysis, see Otter et al. (2017)
    <doi:10.1140/epjds/s13688-017-0109-5>.
    To learn more about how the permutation test is used for
    nonparametric statistical inference in topological data analysis,
    read Robinson & Turner (2017) <doi:10.1007/s41468-017-0008-7>.
    To learn more about how TDAstats calculates persistent homology,
    you can visit the GitHub repository for Ripser, the software that
    works behind the scenes at <https://github.com/Ripser/ripser>.
    This package has been published as Wadhwa et al. (2018)
    <doi:10.21105/joss.00860>.