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.

In high dimension, low sample size (HDLSS) settings, distance concentration phenomena affects the performance of several popular classifiers which are based on Euclidean distances. The behaviour of these classifiers in high dimensions is completely governed by the first and second order moments of the underlying class distributions. Moreover, the classifiers become useless for such HDLSS data when the first two moments of the competing distributions are equal, or when the moments do not exist. In this work, we propose robust, computationally efficient and tuning-free classifiers applicable in the HDLSS scenario. As the data dimension increases, these classifiers yield perfect classification if the one-dimensional marginals of the underlying distributions are different. We establish strong theoretical properties for the proposed classifiers in ultrahigh-dimensional settings. Numerical experiments with a wide variety of simulated examples and analysis of real data sets exhibit clear and convincing advantages over existing methods.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and they often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting in improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. High-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of benchmark data sets from three different databases exhibit advantages of the proposed methods.