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

Hilmar Böhm, Hernando Ombao*, Rainer von Sachs, Jerome Sanes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3754-3763
Number of pages10
JournalJournal of Statistical Planning and Inference
Issue number12
StatePublished - Dec 2010
Externally publishedYes


  • Classification
  • Discrimination
  • Multivariate time series
  • SLEX library
  • SLEX spectrum
  • Shrinkage

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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