6 citations · 15 across the 7 of their papers we have counts for
8 papers
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…
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…
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…
Statistical Inference on Grayscale Images via the Euler-Radon Transform
Kun Meng, Mattie Ji, Jinyu Wang +4
Tools from topological data analysis have been widely used to represent binary images in many scientific applications. Methods that aim to represent grayscale images (i.e., where p…
Hypothesis testing for medical imaging analysis via the smooth Euler characteristic transform
Jinyu Wang, Kun Meng, Fenghai Duan
Shape-valued data are of interest in applied sciences, particularly in medical imaging. In this paper, inspired by a specific medical imaging example, we introduce a hypothesis tes…
Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transform
Kun Meng, Jinyu Wang, Lorin Crawford +1
In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristi…
Population-level Task-evoked Functional Connectivity via Fourier Analysis
Kun Meng, Ani Eloyan
Functional magnetic resonance imaging (fMRI) is a non-invasive and in-vivo imaging technique essential for measuring brain activity. Functional connectivity is used to study associ…
Principal manifold estimation via model complexity selection
Kun Meng, Ani Eloyan
We propose a framework of principal manifolds to model high-dimensional data. This framework is based on Sobolev spaces and designed to model data of any intrinsic dimension. It in…