Title: Localized multivariate FPCA for analyzing dynamic coupling of the heart and brain
Authors: Robert Krafty - University of Pittsburgh (United States) [presenting]
Abstract: Localized-variate functional principal component analysis (LVFPCA) is discussed for finding basis functions that account for most of the variability in a random multivariate process. As opposed to traditional methods, the basis functions found by LVFPCA can be both sparse among variates (i.e. is zero across an entire functional variate) and localized within a variate (i.e. nonzero only within a subinterval of a variate). LVFPCA is formulated as a rank-one based convex optimization problem with matrix L1 and block Frobenius norm based penalties, which induce localization and variate sparsity, respectively. The approach not only provides more accurate estimates of PCs when they are sparse among variates or localized, but it also provides a tool for obtaining more interpretable PCs. The method is motivated by and used to analyze the coupling of EEG and ECG spectral measures during different periods of sleep.