The Department of Mathematical Sciences will host Dr. Harlin Lee of the University of North Carolina at Chapel Hill on Thursday, November 14, from 12:45 p.m. – 1:45 p.m., as part of its math seminar series. Dr. Lee will present “Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging and Optimal Transport.” This free event will take place in Armitage Hall, Room 121. Contact sm1380@camden.rutgers.edu for more information.
Abstract
Capturing data from dynamic processes through cross-sectional measurements is seen in many fields such as computational biology. Trajectory inference deals with the challenge of reconstructing continuous processes from such observations. In this work, we propose methods for B-spline approximation and interpolation of point clouds through consecutive averaging that is instrinsic to the Wasserstein space. Combining subdivision schemes with optimal transport-based geodesic, our methods carry out trajectory inference at a chosen level of precision and smoothness, and can automatically handle scenarios where particles undergo division over time. We rigorously evaluate our method by providing convergence guarantees and testing it on cell data characterized by bifurcations and merges, comparing its performance against state-of-the-art trajectory inference and interpolation methods. The results not only underscore the effectiveness of our method in inferring trajectories, but also highlight the benefit of performing interpolation and approximation that respect the inherent geometric properties of the data.