Persistence kernels for classification: A comparative study

In the last two decades, with the increasing need to analyze big amounts of data, which are usually complex and of high dimension, it was revealed meaningful and helpful to discover further methodologies to provide new information from data. This has brought to the birth of Topological Data Analysis (TDA), whose aim is to extract intrinsic, topological features, related to the so-called "shape of data". Thanks to its main tool, Persistent Homology (PH), it can provide new qualitative information that it would be impossible to extract in any other way. These kinds of features that can be collected in the so-called Persistence Diagram (PD), have been winning in many different applications, mainly related to applied science, improving the performances of models or classifiers, as in our context. Thanks to the strong basis of algebraic topology behind it, the TDA is very versatile and can be applied to data with a priori any kind of structure, as we will explain in the following.