Signal classification by power spectral density: An approach via Riemannian geometry

The power spectral density (PSD) of a signal is often used as a feature for signal classification for which a distance measure must be chosen to compare the similarity between the signal features. We reason that PSD matrices have structural constraints and describe a manifold in the signal space. Thus, instead of the widely used Euclidean distance (ED), a more appropriate measure is the Riemannian distance (RD) on the manifold. Here, we develop a closed-form RD between two PSD matrices on the manifold and also an optimum weighting matrix for the purpose of signal classification. We then apply this new measure for electroencephalogram (EEG) classification for the determination of sleep states and the results are very encouraging.