Classification of multivariate non-stationary signals: The SLEX-shrinkage approach

We develop a statistical method for discriminating and classifying multivariate non-stationary signals. It is assumed that the processes that generate the signals are characterized by their time-evolving spectral matrix-a description of the dynamic connectivity between the time series components. Here, we address two major challenges: first, data massiveness and second, the poor conditioning that leads to numerically unstable estimates of the spectral matrix. We use the SLEX library (a collection of bases functions consisting of localized Fourier waveforms) to extract the set of time-frequency features that best separate classes of time series. The SLEX approach yields readily interpretable results since it is a time-dependent analogue of the Fourier approach to stationary time series. Moreover, it uses computationally efficient algorithms to enable handling of large data sets. We estimate the SLEX spectral matrix by shrinking the initial SLEX periodogram matrix estimator towards the identity matrix. The resulting shrinkage estimator has lower mean-squared error than the classical smoothed periodogram matrix and is more regular. A leave-one out analysis for predicting motor intent (left vs. right movement) using electroencephalograms indicates that the proposed SLEX-shrinkage method gives robust estimates of the evolutionary spectral matrix and good classification results.