Spring Seminar Series - February 28, 2005
University of Minnesota
School of Statistics
College of Liberal Arts
Analysis
of Non-Stationary Time Series: An Overview of the SLEX Methods
Hernando Ombao
Department of Statistics
University of Illinois
Monday, February 28, 2005
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
Many biological and physical signals are non-stationary in nature. For
example, brain waves recorded during an epileptic seizure have
waveforms whose amplitude (variance) and oscillatory behavior (spectral
distribution) change over time. This talk will address some of the
interesting statistical problems in signal processing, namely, (i.)
representation of non-stationary signals and spectral estimation, (ii.)
dimension reduction for massive multivariate non-stationary signals and
(iii.) feature extraction and selection for classification and
discrimination.
I will present an overview of a coherent and unified body of
statistical methods that are based on the SLEX (smooth localized
complex exponentials) library. The SLEX are time-localized Fourier
waveforms with multi-resolution support. The SLEX library provides a
systematic and efficient way of extracting transient spectral and
cross-spectral features. In addition, the SLEX methods are able to
handle massive data sets because they utilize computationally efficient
algorithms. As a matter of practical importance, the SLEX methods give
results that are easy to understand because they are time-dependent
analogues of the classical Fourier methods for stationary signals.
Finally, under the SLEX models, we develop theoretical results of
consistency for spectral estimation and classification.
The SLEX methods will be illustrated brain waves, fMRI time series, a
speech signal and seismic waves. This talk will conclude with open and
challenging problems in signal analysis and the potential of SLEX in
addressing these.