The PI develops a systematic body of methods and models for analyzing massive non-stationary signals. The basic tool is the SLEX library, a collection of bases, each basis consisting of orthogonal localized Fourier waveforms. The SLEX methods give results that are easy to interpret because they are time-dependent analogues of the Fourier spectral analysis of stationary signals. Moreover, the SLEX methods use computationally efficient algorithms, thus, they will be capable of handling massive data sets. The PI develops a family of multivariate models for non-stationary signals recorded from several subjects. The model explicitly takes into account the time-evolving inter-connection between the components of the multivariate signals. In addition, the PI develops an automatic procedure for decomposing the high dimensional multivariate signals into SLEX components using the eigenvalue-eigenvector decomposition of the time-varying SLEX spectral matrix. The SLEX components are non-stationary and have zero-coherency. Thus, they contain non-redundant information on the time-varying cross spectra, which will be used as the primary feature for model selection as well as for discrimination and classification. Finally, the PI develops an automatic and systematic method for extracting time-varying higher order spectral features of non-stationary signals. The PI develops the SLEX higher order spectra, which can account for the time-evolutionary interaction between different frequency components in the signal. In this proposal, the SLEX are the foundation on which the body of coherent and systematic methods for non-stationary signals is built.
This proposal is motivated by the statistical problems that confront the neuroscience community. Major advances in technology now enable neuroscientists to collect complex data sets for investigating the more intricate functioning of the human brain. There is currently a major interest to study how different brain areas interact with each other in response to a mental stimulus. There is also a widespread interest in exploring the association between impairment in brain connectivity and various mental disorders. To study brain connectivity, various types of signals (EEGs, MEGs, fMRI) are recorded. Analyzing brain signals is quite challenging because the brain is a complex organ. Moreover, the signals collected are both non-stationary and massive. The SLEX methods that the PI develops in this proposal address these issues. The SLEX methods are able to capture the local temporal features of the signals. Moreover, the methods are able to handle massive data sets, because they use computationally efficient algorithms. As part of the educational component of this proposal, the PI works closely with graduate and undergraduate students in this research undertaking.
