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

TL;DR

This paper introduces a new method for sparse, localized principal component analysis of high-dimensional multivariate time series in the frequency domain, enabling interpretable insights into complex data such as EEG signals.

Contribution

It proposes a consistent estimation procedure and an efficient algorithm for localized sparse PCA in the frequency domain, tailored for high-dimensional time series analysis.

Findings

Successfully applied to EEG data in psychosis study

Provides interpretable, frequency-localized principal components

Enhances understanding of neurological mechanisms

Abstract

Principal component analysis has been a main tool in multivariate analysis for estimating a low dimensional linear subspace that explains most of the variability in the data. However, in high-dimensional regimes, naive estimates of the principal loadings are not consistent and difficult to interpret. 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, particularly if the principal components are interpretable in that they are sparse in coordinates and localized in frequency bands. In this paper, we introduce a formulation and consistent estimation procedure for interpretable principal component analysis for high-dimensional time series in the frequency domain. An efficient frequency-sequential algorithm is developed to compute sparse-localized estimates of the low-dimensional principal subspaces of the signal process. The method is motivated by and used to understand neurological mechanisms from high-density resting-state EEG in a study of first episode psychosis.