3 papers
math.ST2026
Theoretical Foundations of Principal Manifold Estimation with Non-Euclidean Templates
Kun Meng, Christopher Perez
We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambi…
stat.AP2024
Longitudinal Principal Manifold Estimation
Robert Zielinski, Kun Meng, Ani Eloyan
Longitudinal magnetic resonance imaging data is used to model trajectories of change in brain regions of interest to identify areas susceptible to atrophy in those with neurodegene…
math.AT2023
Euler Characteristics and Homotopy Types of Definable Sublevel Sets, with Applications to Topological Data Analysis
Mattie Ji, Kun Meng
Given a definable function on a definable set , we study sublevel sets of the form for all . U…