Description
This talk will be a review of the efforts of the Topological Data Analysis (TDA) community to design effective features for data, to be used in applications, and to make these features explainable. After a general introduction on TDA, the main focus will be on recent attempts to invert the TDA operator. While this line of work is still in its infancy, the hope on the long run is to use inverses for feature interpretation. The mathematical tools involved in the analysis come mainly from metric geometry, spectral theory, and the theory of constructible functions---specific pointers will be given in the course of the exposition.
