Classification of Spectral Densities of Stationary Time Series

Details

Supervisors

von Sachs, Rainer

Faculty

Faculté des sciences

Degree label

Master [120] en science des données, orientation statistique, à finalité spécialisée

Abstract

This thesis investigates time series classification by analyzing spectral densities within a Riemannian geometric framework. By evaluating advanced distance metrics such as Affine-Invariant Riemannian (AIR), Log-Euclidean, and Whittle distances, this research demonstrates their effectiveness over the traditional Euclidean distance, particularly in managing outliers. Two classification methods, Minimum Distance to Means (MDM) and k-Nearest Neighbors (k-NN), are rigorously assessed using these spectral distances. The study includes both simulated data and real-world EEG signals, revealing that AIR and Log-Euclidean distances, when used with the MDM method, significantly enhance classification accuracy. The thesis advances time series analysis by integrating spectral density comparison with robust geometric techniques, while also identifying potential areas for future research.