- Formulation of interpretable sparse and frequency-localised principal component analysis for high-dimensional multivariate time series in the frequency domain
- Consistent estimation procedure and efficient frequency sequential algorithm to compute sparse localised estimates of low-dimensional principal subspaces
- Application to high-density resting-state EEG reveals interpretable frequency-specific components aiding understanding of neurological mechanisms in first episode psychosis
J Am Stat Assoc. 2026 Jun 4. doi: 10.1080/01621459.2026.2645460. Online ahead of print.
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.
PMID:42434705 | PMC:PMC13354321 | DOI:10.1080/01621459.2026.2645460
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