Functional Principal Component Analysis : A Generalization of Multivariate Principal Component Analysis

Functional Principal Component Analysis : A Generalization of Multivariate Principal Component Analysis

A principal component analysis (PCA) is trying to find a sequence of orthogonal components through a few linear combinations of original variables. The main goal of PCA is data reduction. The term “functional data refers to data, where each observation is a curve. a surface, or a hypersurface. as opposed to a point or a finite-dimensional vector. Functional data are intrinsically infinite dimensional and measurements on the same curve display high correlation, making assumptions of classical multivariate models invalid. In functional principal components (FPCA) we are trying to summarize the infinite dimensional random trajectories through a finite number of functional principal component scores. In this paper, we decide to explain some of the proprieties of PCA and FPCA. The Hilbert space and the proprieties of eigenvalues and eigenvectors (EEP) will be stated, too. Finally, we work on a real data, as an example of FPCA. , Functional Data. Functional Principal Compofultivariate Principal Component Analysis. Eigenvalues. Eigenrum of a Bounded Linear Operator