Date: 2024-10-11

Time: 15:30-16:30 (Montreal time)

Location: In person, Burnside 1104

https://mcgill.zoom.us/j/87824357176

Meeting ID: 878 2435 7176

Passcode: None

Abstract:

The shape $\tilde{\mathbf{X}}$ of a random planar curve, $\mathbf{X}$, is what remains when the deformation variables (scaling, rotation, translation, and reparametrization) are removed. Previous studies in statistical shape analysis have focused on analyzing $\tilde{\bf X}$ through discrete observations of ${\bf X}$. While this approach has some computational advantages, it overlooks the continuous nature of variables: $\tilde{\bf X}$, ${\bf X}$, and it ignores the potential dependence of deformation variables on each other and $\tilde{ \bf X}$, which results in a loss of information in the data structure. I will introduce a new framework for studying $\bf X$ based on functional data analysis in this presentation. Basis expansion techniques are employed to find analytic solutions for deformation variables such as rotation and parametrization deformations. Then, the generative model of $\bf X$ is investigated using a joint-principal component analysis approach. Numerical experiments on synthetic and real datasets demonstrate how this new approach performs better at analyzing random planar curves than traditional functional data methods.

Speaker

Issam Moindjié obtained his PhD in Statistics in 2023 from the University of Lille, France. He has been a postdoctoral researcher at UQAM since June 2024. His current research interests include functional data analysis, statistical shape analysis, and spatial statistics.