Stationary subspace analysis (SSA) is a recent technique for finding linear transformations of nonstationary processes that are stationary in the limited sense that the first two moments or means and lag‐0 covariances are time‐invariant. It finds a matrix that projects the nonstationary data onto a stationary subspace by minimizing a Kullback–Leibler divergence between Gaussian distributions measuring the nonconstancy of the means and covariances across several segments. We propose an SSA procedure for general multivariate, second‐order nonstationary processes. It relies on the asymptotic uncorrelatedness of the discrete Fourier transform of a stationary time series to define a measure of departure from stationarity, which is then minimized to find the stationary subspace. The dimension of the subspace is estimated using a sequential testing procedure, and its asymptotic properties are discussed. We illustrate the broader applicability and better performance of our method in comparison to existing SSA methods through simulations and discuss an application in analyzing electroencephalogram (EEG) data from brain–computer interface (BCI) experiments.
In order to reduce the noise of brain signals, neuroeconomic experiments typically aggregate data from hundreds of trials collected from a few individuals. This contrasts with the principle of simple and controlled designs in experimental and behavioral economics. We use a frequency domain variant of the stationary subspace analysis (SSA) technique, denoted as DSSA, to filter out the noise (nonstationary sources) in EEG brain signals. The nonstationary sources in the brain signal are associated with variations in the mental state that are unrelated to the experimental task. DSSA is a powerful tool for reducing the number of trials needed from each participant in neuroeconomic experiments and also for improving the prediction performance of an economic choice task. For a single trial, when DSSA is used as a noise reduction technique, the prediction model in a food snack choice experiment has an increase in overall accuracy by around 10% and in sensitivity and specificity by around 20% and in AUC by around 30%, respectively.
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