2 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…
math.AT2026
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…