多变量时间序列频域中的局部稀疏主成分分析
Localized Sparse Principal Component Analysis of Multivariate Time Series in Frequency Domain
AI总结：
本文提出一种在频域中对高维时间序列进行可解释主成分分析的方法，通过开发高效的频域序列算法，实现稀疏局部化的主成分估计，用于理解精神分裂症患者的神经机制。
摘要：
主成分分析已成为多变量分析中估计低维线性子空间的主要工具，该子空间能解释数据中大部分变异。然而，在高维情况下，朴素的主成分载荷估计不一致且难以解释。在时间序列中，主成分分析谱密度矩阵可以提供有价值的、简洁的信息，特别是当主成分可解释，即在坐标上稀疏且在频率带中局部化时。本文介绍了一种在频域中对高维时间序列进行可解释主成分分析的公式和一致估计程序。开发了高效的频域序列算法来计算信号过程低维主子空间的稀疏局部估计。该方法受到并用于理解高密度静息态EEG在首次发作精神分裂症研究中的神经机制。
英文摘要：
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 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
