Principal Components Analysis: from multivariate to functional and count data

Abstract

Principal Components Analysis (PCA) is a classical dimension reduction technique that is widely used in various fields, including data science and image analysis. In this talk, we discuss extensions of PCA to data belonging to infinite dimensional spaces. We first focus on functional PCA, which is designed for datasets containing random functions and discuss its extension to datasets containing random measures (such as point processes). We will explore the connection between PCA, the Karhunen-Loève decomposition and some second-order differential equations.