Codes and Expansions (CodEx) Seminar

Akram Aldroubi (Vanderbilt University)
Transport transforms for data analysis and machine learning

A relatively new set of transport-based transforms (CDT, R-CDT, LOT) have shown their strength and great potential in various image and data processing tasks such as parametric signal estimation, classification, cancer detection among many others. In this talk, we will describe the Cumulative Distribution Transform (CDT), its connections to the Monge and Kantorovich problems, and its relation to the Wasserstein metrics. We will elucidate some of the mathematical properties that explain the successes of these transforms when they are used as tools in data analysis, signal processing or data classification. In particular, we give conditions under which classes of signals that are created by algebraic generative models are transformed into convex sets by the transport transforms. We end the talk with some open problems.