An enormous amount of heterogeneous and distributed data, the so-called Big Data, are continuously produced all over the world. Extracting information from such data depends, not only, on an ever greater power of calculation but also on the adoption of innovative techniques.
Topological data analysis (TDA) is a new paradigm for studying the shape of data; in particular, TDA is conceived for obtaining hidden high dimensional patterns from data using topological techniques.
TDA allows to build a discrete topological space in a coordinate free manner, and, using persistent homology, to derive the topological invariants, i.e. the Betti numbers, that characterize that space.
The procedure that allows to obtain discrete topological space is called “filtration” and according to the data domain, different types of filtration can be used.
In this paper the TDA and some case studies in which the TDA has been used successfully will be presented.