Title: A frequency domain approach to stationary subspace analysis of multivariate second-order nonstationary time series
Authors: Raanju Sundararajan - KAUST (Saudi Arabia) [presenting]
Abstract: Transforming high dimensional multivariate nonstationary time series into a lower dimensional stationary time series is of great importance in application areas such as neuroscience and economics. Brain signals like electroencephalograms (EEGs) often appear as nonstationary time series and removing the nonstationarity from the observed signal is useful in building classification models for brain-computer interface. Stationary subspace analysis (SSA) finds instantaneous stationary linear transformations of nonstationary processes. We describe an SSA procedure for multivariate second-order nonstationary processes. The key idea is the property of asymptotic uncorrelatedness of the discrete Fourier transform of a second-order stationary time series. A measure of departure from stationarity that captures the sizes of the entries of the DFT covariance matrices is minimized to obtain the transformation matrix. The dimension of the subspace is estimated using a sequential procedure and its asymptotic properties are provided. The non-uniqueness issues in subspace estimation are discussed and a technique to select a subspace from a set of subspaces using canonical angles is provided. We study the performance of the method in detecting the dimension of the true subspace through simulation examples. Finally, we present an application of SSA in constructing a classification model that differentiates healthy subjects from subjects with some neurological disorder.