Classification of High-dimensional Time Series in Spectral Domain Using Explainable Features with Applications to Neuroimaging Data

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which can be restrictive for real-world applications. We propose a model-based approach for classifying high-dimensional stationary time series by assuming sparsity in the difference between inverse SDMs. The estimators for model parameters possess consistency under fairly general conditions. Additionally, we introduce a method to screen the most discriminatory frequencies for classification, which exhibits the ${\it sure\ screening\ property}$. The novelty of our method lies in the interpretability of the model parameters, making it especially suitable for fields like neuroscience, where understanding differences in brain network connectivity across various states is crucial. The proposed approach is evaluated using a variety of simulated examples. We apply it to EEG and calcium imaging datasets to demonstrate its practical relevance.