Localized Sparse Principal Component Analysis of Multivariate Time Series in the Frequency Domain
提出一种频域方法，对高维时间序列进行稀疏且局部化的主成分分析，通过高效算法估计低维主子空间，用于理解首次发作精神病患者的静息态脑电图数据。
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.