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

Sarbojit Roy, Malik Shahid Sultan, Tania Reyes Vallejo, Leena Ali Ibrahim, Hernando Ombao

TL;DR: We propose a convex optimization method and a probabilistic model to learn the most discriminative features between two classes of high-dimensional time series.

Abstract: Interpretable classification of time series poses significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral matrices (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 spectra. The estimators for the model parameters are proven to be consistent under general conditions. We also introduce a method to select the most discriminatory frequencies, and it possesses the sure screening property. The novelty of our method lies in the interpretability of the parameters hence suitable for neuroscience where understanding differences in brain network connectivity across various states is crucial. The proposed approach is tested using several simulated examples and applied to EEG and calcium imaging datasets to demonstrate its practical relevance.

Submission Number: 726