Learning Topology: Bridging Computational Topology and Machine Learning

Topology is a classical branch of mathematics, born essentially from Euler’s studies in the XVII century, which deals with abstract notion shape and geometry. Last decades were characterized by renewed interest topology topology-based tools, due to birth computational topological data analysis (TDA). A large novel family methods algorithms computing features descriptors (e.g., persistent homology) have proved be effective tools for graphs, 3D objects, 2D images, even heterogeneous datasets. This survey intended concise but complete compendium that, offering essential basic references, allows you orient yourself among recent advances TDA its applications, an eye those related machine learning deep learning.