Hernando Ombao (UC Irvine, Dept of Statistics)
Problems in Non-Stationary Multivariate Time Series With Applications in Brain Signals

We present new tools for analyzing complex multichannel signals using spectral methods. The key challenges are the high dimensionality of brain signals, massive size and the complex nature of the underlying physiological process – in particular, non-stationarity. In this talk, I will highlight some of the current projects. The first is a tool that identifies changes in the structure of a multivariate time series. This is motivated by problems in characterizing changes in brain signals during an epileptic seizure where a localized population of neurons

exhibits abnormal firing behavior which then spreads to other subpopulations of neurons. This abnormal firing behavior is captured by increases in signal amplitudes (which can be easily spotted by visual inspection) and changes in the decomposition of the waveforms and in the strength of dependence between different regions (which are more subtle). The proposed frequency-specific change-point detection method (FreSpeD) uses a cumulative sum test statistic within a binary segmentation algorithm. Theoretical optimal properties of the FreSpeD method will be developed. We demonstrate that, when applied to an epileptic seizure EEG data, FreSpeD identifies the correct brain region as the focal point of seizure, the time of seizure onset and the very subtle changes in cross-coherence immediately preceding seizure onset.

The goal of the second project to track changes in spatial boundaries (or more generally spatial sets or clusters) as the seizure process unfolds. A pair of channels (or a pair of sets of channels) are merged into one cluster if they exhibit synchronicity as measured by, for example, similarities in their spectra or by the strength of their coherence. We will highlight some open problems including developing a model for the evolutionary clustering of non-stationary time series.

The first project is in collaboration with Anna Louise Schröder (London School of Economics); the second is with Carolina Euan (CIMAT, Mexico), Joaquin Ortega (CIMAT, Mexico) and Ying Sun (KAUST, Saudi Arabia).