A new methodology for Functional Principal Component Analysis from scarce data. Application to stroke rehabilitation

Functional Principal Component Analysis (FPCA) is an increasingly used methodology for analysis of biomedical data. This methodology aims to obtain Functional Principal Components (FPCs) from Functional Data (time dependent functions). However, in biomedical data, the most common scenario of this analysis is from discrete time values. Standard procedures for FPCA require obtaining the functional data from these discrete values before extracting the FPCs. The problem appears when there are missing values in a non-negligible sample of subjects, especially at the beginning or the end of the study, because this approach can compromise the analysis due to the need to extrapolate or dismiss subjects with missing values. In this paper, we present an alternative methodology extracting the FPCs directly from the sampled data, avoiding the need to have functional data before extracting them. We demonstrate the feasibility of our approach from real data obtained from the analysis of balance recovery after stroke. Finally, we demonstrate that FPCA can obtain differences between groups when these differences are more related to the dynamics of the process than data values at given points.