Detecting Determinism in EEG Signals using Principal Component Analysis and Surrogate Data Testing

A novel method is proposed here to determine whether a time series is deterministic even in the presence of noise. The method is the extension of an existing method based on smoothness analysis of the signal in state space with surrogate data testing. While classical measures fail to detect determinism when the time series is corrupted by noise, the proposed method can clearly distinguish between pure stochastic and originally deterministic but noisy time series. A set of measures is defined here named partial smoothness indexes corresponding to principal components of the time series in state space. It is shown that when the time series is not pure stochastic, at least one of the indexes reflects determinism. The method is first successfully tested through simulation on a chaotic Lorenz time series contaminated with noise and then applied on EEG signals. Testing results on both our experimental recorded EEG signals and a benchmark EEG database verifies this hypothesis that EEG signals are deterministic in nature while contain some stochastic components as well.