Codes and Expansions (CodEx) Seminar

Brantley Vose (The Ohio State University)
The Limits of Vectorization: Euclidean Distortion of Orbit Spaces

Many machine learning techniques are designed to work with vector data. At the same time, many common forms of data, such as shapes, graphs, and databases, naturally live in orbit spaces that do not admit obvious embeddings into Euclidean space. Translating such data types into vectors is called vectorization and it often requires one to distort the natural geometry of the data space. In this talk, we will explore this geometric distortion problem for various orbit spaces. We will discuss tools and strategies for zeroing in on the optimal distortion for such a space.