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

• 成果类型: Article; Early Access
• 署名作者: Namdari, Jamshid; Manatunga, Amita; Ferrarelli, Fabio; Krafty, Robert T.
• 署名单位: Emory University; Rollins School Public Health; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2645460
• 发表日期: 2026-05-26
• 关键词: Frequency band; High dimensional time series; Principal Component Analysis; Sparse Estimation; spectral density matrix; PCA

摘要

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 article, 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.