Functional Principal Component Analysis

‪Frédéric PROTIN
Mathematician, Torus AI, PhD
July 6th, 2023

Abstract
Functional PCA is a generalization of the PCA method of dimension reduction, when the data no longer necessarily lives in ℝⁿ but in a separable Hilbert space. In concrete terms, these are curves resulting from measurements. This introductory talk exposes the mathematical foundations of functional PCA. To this end, we present some spectral properties of operators, and of the Bochner integral. A proposal for an application to the analysis of financial data, in connection with AI, is then presented.