Dimensionality Reduction of Multivariate Functional Data Using FPCA

Abstract

In many scientific and engineering applications, data are collected over discrete, often equidistant, time intervals. While such data can be analyzed using traditional statistical methods, these methods are often very limited in their ability to capture the underlying continuous nature of dynamic processes of the phenomenon under study. This study aims to present and develop a statistical methodology for analysing multivariate functional data characterised by structural complexity, nonlinear properties, and continuous nature of its observations and variables. By using the Functional Principal Component Analysis (FPCA) method to analyse high-dimensional data through dimensionality reduction, and accurately discovering structural patterns in the data without relying on fixed distributional assumptions. Also, improving model selection using the Bayesian Information Criterion (BIC), which determines the optimal number of orthogonal basis functions and enhances the model's fit to the complexity of the data, thereby contributing to the accuracy of the analysis and understanding of relationships within the functional data.