most citedEuler Characteristics and Homotopy Types of Definable Sublevel Sets, with Applications to Topological Data Analysis

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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…