A Koopman-operator-theoretical approach for anomaly recognition and detection of multi-variate EEG system

For most real-life dynamical systems, it is difficult to explicitly identify evolution rules or functions that describe the complex, non-linear, and non-stationary patterns of dynamical systems. Alternatively, it is common to describe and analyze the system dynamics through observations, e.g., electroencephalography (EEG) signals are observed and used for representing the brain system. Even though, the underlying dynamics of the system is still not easily uncovered and displayed as a whole. In this study, we propose a data-driven approach based on the Koopman operator to reconstruct and analyze the underlying dynamics of dynamical systems by representing them in a linear intrinsic space. To demonstrate the applicability, we apply the proposed method to dynamical pattern recognition problems, and validate it with a simulation study of the Lorenz system and a brain disorder of epileptic seizure using multi-variate EEG signals. Furthermore, we introduce a new measurement that is derived from the reconstructed dynamics associated with the attractor of the system in the Koopman intrinsic space. The experimental results conclude the effectiveness of the proposed method for anomaly detection using the reconstructed dynamical information.