Modeling High-Dimensional Multichannel Brain Signals

Hu, Lechuan; Fortin, Norbert J.; Ombao, Hernando

doi:10.1007/s12561-017-9210-3

Cited by 15 publications

(8 citation statements)

References 23 publications

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“…Although different forms of

Ψ_{n}

can be considered depending on the application, sparse forms provide computationally reasonable choices, with the diagonal structure being the most commonly used (Basu and Michailidis, 2015; Hu et al ., 2017; Lin and Michailidis, 2017). In particular, choosing

Ψ_{n} = α_{n} 𝕀_{d}

, with

α_{n}

a scalar and

𝕀_{d}

the

d \times d

identity matrix, corresponds to the case where the cross‐covariance between two observation points ( i and j ) at times

t_{n}

and

t_{n + 1}

is a fraction (

α_{n}

) of the covariance between those two points at time

t_{n}

(i.e.,

cov (v_{i, n + 1}, v_{j, n}) = α_{n} cov (v_{i, n}, v_{j, n})

).…”

Section: Problem Formulationmentioning

confidence: 99%

Ensemble Kalman filtering with coloured observation noise

Raboudi

Ait‐El‐Fquih

Ombao

et al. 2021

Quart J Royal Meteoro Soc

Self Cite

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The Kalman filter (KF) is derived under the assumption of time-independent (white) observation noise. Although this assumption can be reasonable in many ocean and atmospheric applications, the recent increase in sensor coverage, such as the launching of new constellations of satellites with global spatio-temporal coverage, will provide high density of oceanic and atmospheric observations which are expected to have time-dependent (coloured) error statistics. In this situation, the KF update has been shown to generally provide overconfident probability estimates, which may degrade the filter performance. Different KF-based schemes accounting for time-correlated observation noise were proposed for small systems by modelling the coloured noise as a first-order autoregressive model driven by white Gaussian noise. This work introduces new ensemble Kalman filters (EnKFs) which account for coloured observational noises for efficient data assimilation into large-scale oceanic and atmospheric applications.More specifically, we follow the standard and the one-step-ahead smoothing formulations of the Bayesian filtering problem with coloured observational noise, modelled as an autoregressive model, to derive two (deterministic) EnKFs. We demonstrate the relevance of the coloured observational noise-aware EnKFs and analyze their performances through extensive numerical experiments conducted with the Lorenz-96 model.

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“…Although different forms of

Ψ_{n}

Ψ_{n} = α_{n} 𝕀_{d}

, with

α_{n}

a scalar and

𝕀_{d}

the

d \times d

identity matrix, corresponds to the case where the cross‐covariance between two observation points ( i and j ) at times

t_{n}

and

t_{n + 1}

is a fraction (

α_{n}

) of the covariance between those two points at time

t_{n}

(i.e.,

cov (v_{i, n + 1}, v_{j, n}) = α_{n} cov (v_{i, n}, v_{j, n})

).…”

Section: Problem Formulationmentioning

confidence: 99%

Ensemble Kalman filtering with coloured observation noise

Raboudi

Ait‐El‐Fquih

Ombao

et al. 2021

Quart J Royal Meteoro Soc

Self Cite

View full text Add to dashboard Cite

show abstract

“…Among them, matrix‐valued data are commonly encountered in brain images and signals, where the sampling unit can be viewed as a two‐dimensional array (ie, matrix), for example, electroencephalography (EEG) and local field potentials (LFPs). These signals are in general high‐dimensional and possess complicated structure such as spatial/temporal correlation, low rankness, and sparsity (Gao et al ., 2019; Hu et al ., 2019; Wang et al ., 2019). The main goal of this paper is to provide a novel approach for clustering matrix‐valued data while taking their complex structure into account.…”

Section: Introductionmentioning

confidence: 99%

Regularized matrix data clustering and its application to image analysis

Shen

Zhang

et al. 2020

Biometrics

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We propose a novel regularized mixture model for clustering matrix-valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (e.g., low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix-normal distributions with regularization terms, and then develop an EM-type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of the solution.

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“…Note that the system's dimensionality increases substantially with 144pm 2 coefficients needed to be estimated. To provide an efficient regularization approach to estimate the model parameters, we rely on the method LASSLE proposed by Hu et al [14]. The latter consists of executing the estimation in two phases: a) identify the relevant covariates using a LASSO regression, and b) use an ordinary least square to estimate the coefficients and their uncertainty.…”

Section: Causality Modelingmentioning

confidence: 99%

SCAU: Modeling spectral causality for multivariate time series with applications to electroencephalograms

Pinto-Orellana,

Mirtaheri,

Hammer

et al. 2021

Preprint

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Electroencephalograms (EEG) are noninvasive measurement signals of electrical neuronal activity in the brain. One of the current major statistical challenges is formally measuring functional dependency between those complex signals. This paper, proposes the spectral causality model (SCAU), a robust linear model, under a causality paradigm, to reflect inter-and intrafrequency modulation effects that cannot be identifiable using other methods. SCAU inference is conducted with three main steps: (a) signal decomposition into frequency bins, (b) intermediate spectral band mapping, and (c) dependency modeling through frequency-specific autoregressive models (VAR). We apply SCAU to study complex dependencies during visual and lexical fluency tasks (word generation and visual fixation) in 26 participants' EEGs. We compared the connectivity networks estimated using SCAU with respect to a VAR model. SCAU networks show a clear contrast for both stimuli while the magnitude links also denoted a low variance in comparison with the VAR networks. Furthermore, SCAU dependency connections not only were consistent with findings in the neuroscience literature, but it also provided further evidence on the directionality of the spatio-spectral dependencies such as the delta-originated and theta-induced links in the fronto-temporal brain network.

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Modeling High-Dimensional Multichannel Brain Signals

Cited by 15 publications

References 23 publications

Ensemble Kalman filtering with coloured observation noise

Ensemble Kalman filtering with coloured observation noise

Regularized matrix data clustering and its application to image analysis

SCAU: Modeling spectral causality for multivariate time series with applications to electroencephalograms

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