Events for 09/16/2021 from all calendars
Seminar on Banach and Metric Space Geometry
Time: 11:00AM - 12:00PM
Location: BLOC 302
Speaker: Keaton Hamm, UT Arlington
Title: Optimal transport methods in nonlinear dimensionality reduction
Abstract: The manifold hypothesis, that high-dimensional data lives on or near a low-dimensional embedded manifold, is ubiquitous in machine learning theory and practice. For imaging data, the data appears as vectors in high-dimensional Euclidean space, where the vectors are acquired from some imaging operator mapping a functional space, such as L2, to Euclidean space. It is unclear that Euclidean distance between the image vectors contains sufficient semantic meaning to understand the structure of the functional data manifold. We consider treatment of the functional data as a set of probability measures, and use pairwise Wasserstein distances to compute similarity. We then utilize these distances in the ISOMAP algorithm for nonlinear dimensionality reduction. We show how the proposed algorithm, WassMap, recovers translational and dilational functional manifolds up to global isometry. We also show further experiments on synthetic data which illustrate the methods success on a variety of other kinds of image manifolds.
Committee P & IP Meeting
Time: 4:00PM - 5:00PM
Location: ZOOM
, Texas A&M UniversitySeptember Math Club Meeting
Undergraduate Calendar
Time: 7:30PM - 9:00PM
Location: Blocker 166
Speaker: Dr. Yasskin, Texas A&M Math Department
Description: King Arthur Problem activity