From Topological Data Analysis to Deep Learning: No Pain No Gain

Today, I'll try to give some insights about TDA (for Topological Data Analysis), a mathematical field quickly evolving, that will certainly soon be completely integrated into machine-/deep- learning frameworks. Some use-cases will be presented in the wake of this article, in order to illustrate the power of that theory! Topological Data Analysis, also abbreviated TDA, is a recent field that emerged from various works in applied topology and computational geometry. It aims at providing well-founded mathematical, statistical and algorithmic methods to exploit the topological and underlying geometric structures in data. You will generally find it suitable for three-dimensional data, but experience shows that TDA reveals also to be useful in other cases, such as time-series.