Title: Classification of Categorical Time Series Using the Spectral Envelope and Optimal Scalings
Abstract: This work introduces a novel approach to the classification of categorical time series under the supervised learning paradigm. To construct meaningful features that can be used for categorical time series classification, we consider two relevant quantities: the spectral envelope and its corresponding set of optimal scalings. These quantities characterize oscillatory patterns in a categorical time series as the largest possible power at each frequency, or spectral envelope, obtained by assigning numerical values, or scalings, to categories that optimally emphasize oscillations at each frequency. Our procedure combines these two quantities to produce an interpretable and parsimonious feature-based classifier that can be used to accurately determine group membership for categorical time series. Using a training set of time series with known group membership, we first estimate spectral envelope- and scaling-based features for each group. Then, these features are estimated individually for time series with unknown group membership, and time series are classified to the group with the most similar estimated features. Classification consistency of the proposed method is investigated, and simulation studies are used to demonstrate accuracy in classifying time series with various underlying group structures. Finally, we use the proposed method to explore oscillatory patterns of sleep stage time series obtained from patients with nocturnal frontal lobe epilepsy and REM behavior disorders, and accurately classify those patients.