Topological data analysis (TDA) is at the crossroad of data analysis, algebraic topology, computational geometry, computer science, statistics, and other related areas.

TDA studies qualitative features of data using results from geometry and topology. To achieve this goal, the qualitative features need precise definitions, tools to compute them in practice, and some guarantee about their robustness.

Due to the dramatically increase of the amount of data, the situation requires more efficient data-processing methods.

A method in TDA that fulfils these conditions is called persistent homology.