Why Topology for Machine Learning and Knowledge Extraction?

Data has shape, and shape is the domain of geometry and in particular of its “free” part, called topology. The aim of this paper is twofold. First, it provides a brief overview of applications of topology to machine learning and knowledge extraction, as well as the motivations thereof. Furthermore, this paper is aimed at promoting cross-talk between the theoretical and applied domains of topology and machine learning research. Such interactions can be beneficial for both the generation of novel theoretical tools and finding cutting-edge practical applications.