A0878
Title: Bridging geometry and statistics: PCA for directional data
Authors: Anahita Nodehi - University of Bristol (United Kingdom) [presenting]
Meisam Moghimbeygi - Kharazmi University (Iran)
Christophe Ley - University of Luxembourg (Luxembourg)
Abstract: High-dimensional data often present significant challenges in statistical analysis, including difficulties in visualization, increased computational complexity, and a higher probability of overfitting or underfitting. These issues are further compounded by the curse of dimensionality, which states that the number of observations required for accurate modeling grows exponentially as the number of dimensions increases. To address these challenges, dimension reduction techniques are commonly employed. Principal component analysis (PCA) is one of the most widely used dimension reduction techniques and has been extensively studied within classical linear (Euclidean) spaces. However, in many applied fields such as biology, bioinformatics, astronomy, and geology, data often lie in non-Euclidean spaces, specifically on Riemannian manifolds such as the unit circle, sphere, or torus. In these contexts, data are referred to as manifold-valued or directional data. When working with directional data, the linear assumptions underlying PCA may limit its effectiveness for accurate dimension reduction. The purpose is to review and investigate the methodological developments of PCA for directional data and explore their practical applications.
