Sparse Separable Factor Analysis in the Complex Domain with an Application to Local Field Potential Data

2026-08-21

AI Summary

本文提出稀疏可分离因子分析(SSFA)，针对复数域信号处理中幅度和相位信息的保留问题，通过低秩Hermitian结构及对角残差协方差矩阵建模，并采用lasso惩罚获得可解释估计。

Abstract

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.

Problem

• Complex-valued arrays
• Covariance estimation
• Separable covariance structure
• Latent factor model

Innovation

• Sparse Separable Factor Analysis
• Complex-valued Arrays
• Hermitian Factor Structure
• Lasso Penalties
• Parameter-expanded Expectation-Maximization