Sophie Dabo (Univ. Lille) : Functional Data Analysis: A PCA Approach for Learning Models and Applications to Biology

Functional data, representing observations from complex processes, present significant challenges in modeling non-stationary time or spatially dependent phenomena such as curves, shapes, images, and other intricate structures. This talk focuses on Principal Component Analysis (PCA) tailored for complex functional datasets, including case-control studies, time series, and spatial data. We will explore the interplay between the functional characteristics and the inherent dependencies in the data, revealing underlying structures and patterns in stratified, spatial, or space-time datasets. We will provide an overview of complex functional data, emphasizing their prevalence across diverse domains like environmental monitoring, geostatistics, and biomedical research. A key focus will be on the theoretical foundations of Functional Principal Component Analysis, highlighting its flexibility in analyzing dependent data. We will present practical applications of functional PCA, particularly in identifying temporal or spatial dependencies, capturing variability, and reducing dimensionality. Real-world case studies will demonstrate the effectiveness of these techniques in various contexts. Finally, we will address challenges associated with applying PCA to learning from complex functional data, such as managing infinite sample properties, data dependency, large datasets, computational demands