Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals

Raanju R. Sundararajan,Hernando Ombao,Ron Frostig

doi:10.3390/e22121375

Abstract

In some applications, it is important to compare the stochastic properties of two multivariate time series that have unequal dimensions. A new method is proposed to compare the spread of spectral information in two multivariate stationary processes with different dimensions. To measure discrepancies, a frequency specific spectral ratio (FS-ratio) statistic is proposed and its asymptotic properties are derived. The FS-ratio is blind to the dimension of the stationary process and captures the proportion of spectral power in various frequency bands. Here we develop a technique to automatically identify frequency bands that carry significant spectral power. We apply our method to track changes in the complexity of a 32-channel local field potential (LFP) signal from a rat following an experimentally induced stroke. At every epoch (a distinct time segment from the duration of the experiment), the nonstationary LFP signal is decomposed into stationary and nonstationary latent sources and the complexity is analyzed through these latent stationary sources and their dimensions that can change across epochs. The analysis indicates that spectral information in the Beta frequency band (12–30 Hertz) demonstrated the greatest change in structure and complexity due to the stroke.

Highlights

IntroductionNumerous applications require comparing two multivariate time series of unequal dimensions.Neuroscience experiments result in a stationary or nonstationary multivariate signal from different epochs (distinct non-overlapping successive time segments of the duration of the experiment)
Numerous applications require comparing two multivariate time series of unequal dimensions.Neuroscience experiments result in a stationary or nonstationary multivariate signal from different epochs
We proposed a new frequency-specific spectral ratio statistic FS-ratio that is demonstrated to be useful in comparing spectral information in two multivariate stationary processes of different dimensions

Summary

Introduction

Numerous applications require comparing two multivariate time series of unequal dimensions.Neuroscience experiments result in a stationary or nonstationary multivariate signal from different epochs (distinct non-overlapping successive time segments of the duration of the experiment). A popular approach to modeling such data decomposes the observed signal at every epoch into useful latent sources that can be stationary or nonstationary. These latent sources are lower dimensional time series obtained by linear transforms of the components of the observed multivariate series and they aim to capture important statistical properties of the observed series. At these epochs, dimension reduction techniques such as principal component analysis (PCA), factor modeling, independent component analysis (ICA), stationary subspace analysis (SSA) are often applied to extract useful lower-dimensional latent sources. Setting the dimension of these latent sources to be the same across the epochs results in loss of important information

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