Delay Differential Analysis of Electroencephalographic Data

Lainscsek, Claudia; Hernandez, Manuel E.; Poizner, Howard; Sejnowski, Terrence J.

doi:10.1162/neco_a_00656

Cited by 13 publications

(11 citation statements)

References 23 publications

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“…An electroencephalogram (EEG) is a nonintrusive measurement of brain activity achieved through electrodes placed on the scalp. A time series of voltage is recorded from these electrodes, and although typically the spectral content of EEG is analyzed, there are also numerous examples of time series EEG analysis [77,3,47,92,60]. Although it is possible to obtain vast quantities of data, possibly using an array of electrodes, the voltage signal is only a rough proxy for brain activity, as signals must pass through thick layers of dura, cerebrospinal fluid, skull, and scalp.…”

Section: Electroencephalogram (Eeg)mentioning

confidence: 99%

Chaos as an intermittently forced linear system

et al. 2017

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Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth’s magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.

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Section: Electroencephalogram (Eeg)mentioning

confidence: 99%

Chaos as an intermittently forced linear system

et al. 2017

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“…In a companion paper (Lainscsek, Hernandez, Poizner, & Sejnowski, 2015), the methods are applied to electroencephalography (EEG) data.…”

Section: Introductionmentioning

confidence: 99%

Delay Differential Analysis of Time Series

Lainscsek

Sejnowski

2015

Neural Computation

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Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis.

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“…() used delay‐embedded matrices to estimate data components (spatiotemporal coefficients) that link data at each time point to data at the previous time point. Lainscsek and Sejnowski (Lainscsek & Sejnowski, ; Lainscsek et al ., ) used delay‐embedded matrices to model neural dynamics as delay differential equations to estimate frequency‐specific responses and couplings between electrodes. Delay‐embedding matrices are a powerful method for uncovering dynamics in time series data, and continued methodological development and applications will improve the quality of neuroscience data analysis.…”

Section: Discussionmentioning

confidence: 99%

Using spatiotemporal source separation to identify prominent features in multichannel data without sinusoidal filters

Cohen

2017

Eur J of Neuroscience

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The number of simultaneously recorded electrodes in neuroscience is steadily increasing, providing new opportunities for understanding brain function, but also new challenges for appropriately dealing with the increase in dimensionality. Multivariate source separation analysis methods have been particularly effective at improving signal-to-noise ratio while reducing the dimensionality of the data and are widely used for cleaning, classifying and source-localizing multichannel neural time series data. Most source separation methods produce a spatial component (that is, a weighted combination of channels to produce one time series); here, this is extended to apply source separation to a time series, with the idea of obtaining a weighted combination of successive time points, such that the weights are optimized to satisfy some criteria. This is achieved via a two-stage source separation procedure, in which an optimal spatial filter is first constructed and then its optimal temporal basis function is computed. This second stage is achieved with a time-delay-embedding matrix, in which additional rows of a matrix are created from time-delayed versions of existing rows. The optimal spatial and temporal weights can be obtained by solving a generalized eigendecomposition of covariance matrices. The method is demonstrated in simulated data and in an empirical electroencephalogram study on theta-band activity during response conflict. Spatiotemporal source separation has several advantages, including defining empirical filters without the need to apply sinusoidal narrowband filters.

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Delay Differential Analysis of Electroencephalographic Data

Cited by 13 publications

References 23 publications

Chaos as an intermittently forced linear system

Chaos as an intermittently forced linear system

Delay Differential Analysis of Time Series

Using spatiotemporal source separation to identify prominent features in multichannel data without sinusoidal filters

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