Description:

Dimensionality Reduction via t-SNE/UMAP/... -- an overview

Stefan Steinerberger, PhD

Assistant Professor of Mathematics, University of Washington, Seattle

Zoom Link: Contact Tiffany Leighton Ozmina tiffany.ozmina@northwestern.edu for the link

Abstract:    t-SNE, introduced in 2008, is a very popular dimensionality reduction method.  Interestingly, there is barely any mathematical theory explaining why it works (which is a bit troublesome because in many settings it doesn't). George Linderman and I provided the first analysis based on interpreting this as an attraction-repulsion problem (all the little data points talk to each other).  This perspective has proven quite fruitful  -- in fact, it appears that t-SNE is merely a representative of an entire family of algorithms that also includes UMAP, forceatlas2, SNE.... that are all based on the idea of finding an equilibrium between attraction and repulsion between the data points. This perspective naturally suggests MANY other algorithms that might be just as good and that are waiting to be discovered.