复域中的稀疏可分因子分析及其在局部场电位数据中的应用
Sparse Separable Factor Analysis in the Complex Domain with an Application to Local Field Potential Data
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中文总结 AI 辅助
本文提出复域稀疏可分因子分析（SSFA）模型，通过复软阈值等方法实现协方差估计优化，并将其应用于小鼠局部场电位数据的可分结构分析与缺失记录插补。
中文摘要 AI 辅助
复值数组出现在信号处理领域，其科学解释依赖于保留幅度和相位信息。现有协方差估计方法要么忽略此类数据的多路组织，要么依赖实域嵌入，无法直接利用其复结构。我们提出稀疏可分因子分析（Sparse Separable Factor Analysis, SSFA），这是一种针对复值数组的潜在因子模型，具有跨模态的可分协方差结构。每个模态特定的协方差矩阵通过低秩Hermitian因子结构和对角残差协方差矩阵建模。为获得可解释的估计，我们对复载荷矩阵施加逐元素lasso惩罚，并采用模态扩展参数的期望最大化过程估计SSFA参数。所得载荷更新具有闭式复软阈值解，该解在保留每个载荷相位的同时收缩其幅度。单独的平衡步骤解决了可分协方差结构的尺度非识别性问题。模拟研究表明，与向量化方法（包括复主成分分析）相比，SSFA可改进协方差估计。我们将SSFA应用于小鼠的局部场电位记录，比较由不同脑区分组、频率和时间诱导的可分结构，并对因电极错位而缺失的记录进行基于模型的插补。
英文摘要
Complex-valued arrays arise in signal processing, where scientific interpretation depends on retaining amplitude and phase information. Existing covariance estimation methods either ignore the multiway organization of such data or rely on real-domain embeddings that do not directly exploit their complex structure. We develop sparse separable factor analysis (SSFA), a latent factor model for complex-valued arrays with a separable covariance structure across modes. Each mode-specific covariance matrix is modeled through a low-rank Hermitian factor structure and a diagonal residual covariance matrix. To obtain interpretable estimates, we impose elementwise lasso penalties on the complex loading matrices and estimate the SSFA parameters using a mode-wise parameter-expanded expectation-maximization procedure. The resulting loading updates admit closed-form complex soft-thresholding solutions, which shrink the modulus of each loading while preserving its phase. A separate balancing step resolves the scale nonidentifiability of the separable covariance structure. Simulation studies show that SSFA improves covariance estimation relative to vectorization-based methods, including complex principal component analysis. We apply SSFA to local field potential recordings from mice, where we compare separability structures induced by different groupings of brain region, frequency, and time and perform model-based imputation of recordings missing because of electrode misplacement.
发表机构
- University of Iowa（爱荷华大学）
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