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 …

Phat is an open-source C++ library for the computation of persistent homology by matrix
reduction, targeted towards developers of software for topological data analysis. We aim for …

Topological data analysis (TDA)(Edelsbrunner & Harer, 2010),(Carlsson, 2009) is a field
focused on understanding the shape and structure of data by computing topological …

Many data sets can be viewed as a noisy sampling of an underlying space, and tools from
topological data analysis can characterize this structure for the purpose of knowledge …

We present a parallel algorithm for computing the persistent homology of a filtered chain
complex. Our approach differs from the commonly used reduction algorithm by first …

This paper introduces persistent homology, which is a powerful tool to characterize the
shape of data using the mathematical concept of topology. We explain the fundamental idea …

Computational topology has recently seen an important development toward data analysis,
giving birth to Topological Data Analysis. Persistent homology appears as a fundamental …

In this paper we present an efficient framework for computation of persistent homology of
cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is …

Persistent homology (PH) provides topological descriptors for geometric data, such as
weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …

Persistent homology captures the evolution of topological features of a model as a
parameter changes. The most commonly used summary statistics of persistent homology are …