Localized Sparse Principal Component Analysis of Multivariate Time Series in Frequency Domain

Oregon Convention Center 

In the context of time series, principal component analysis of spectral density matrices can provide valuable, parsimonious information about the behavior of the underlying process. Given a high-dimensional weakly stationary time series, it is of interest to obtain principal components of the spectral density matrices that are interpretable as being sparse in coordinates and localized in frequency. In this talk, we introduce a formulation of this novel problem and an algorithm for estimating the object of interest. In addition, we propose a smoothing procedure that improves estimation of eigenvector trajectories over the frequency range. The method is motivated by and used to understand neurological mechanisms from high-density resting-state EEG in a patient hospitalized for a first psychotic episode and compared with a healthy control individual.

Principal component Analysis

Spectral density matrix

High dimensional time series

Sparse Estimation 

Section on Statistics in Imaging