Proposal Description

In the dynamic and ever-expanding field of data science, the analysis of geometric and object data, characterized by their origins from spaces lacking a vector structure, has emerged as a critical frontier. This specialized domain extends beyond traditional Euclidean spaces to address the intricacies of data situated on manifolds, graphs, and various other geometric spaces. As such, it encompasses a wide array of applications, from computer vision and medical imaging to network analysis and beyond.

In light of the growing importance and the unique challenges presented by geometric and object data analysis, we propose organizing this dedicated session on geometric and object data analysis at the forthcoming WSC 2025. The proposed session will feature presentations from five leading experts and emerging young researchers in this field, each bringing their latest research findings to the session. The presentations will cover a broad spectrum of topics integral to the understanding and advancement of geometric and object data analysis. Specifically, the topics in the session encompass:

* Fundamentals of Random Objects: Including characterising the laws governing random objects and investigating large deviations of Fréchet means within Riemannian manifolds.
* Statistical Inference: Developing cutting-edge methods in statistical inference, such as testing predictor effects in global Fréchet regression, which is of practical importance in analyzing complex data.
* Regression for Non-Euclidean Variables: Exploring the challenges and techniques in high-dimensional regression when dealing with variables residing in nonlinear metric spaces.
* Statistics in Important Spaces: Investigating the statistical properties of data in specific spaces of interest, such as the study of random flows of covariances within the Bures-Wasserstein space, which could illuminate understanding in fields like brain connectivity analysis.

We are confident that this dedicated session will enable researchers in geometric and object data analysis to 1) share their latest research findings and methodological advancements, 2) discuss the challenges and opportunities unique to non-Euclidean data, 3) explore interdisciplinary applications and implications of geometric data analysis, 4) foster collaborations and set a forward-looking agenda for research in this field, and 5) ultimately advance the boundaries of knowledge in geometric and object data analysis.