Bi-Smoothed Functional Independent Component Analysis for EEG Artifact Removal

Abstract

Motivated by mapping adverse artifactual events caused by body movements in electroencephalographic (EEG) signals, we present a functional independent component analysis based on the spectral decomposition of the kurtosis operator of a smoothed principal component expansion. A discrete roughness penalty is introduced in the orthonormality constraint of the covariance eigenfunctions in order to obtain the smoothed basis for the proposed independent component model. To select the tuning parameters, a cross-validation method that incorporates shrinkage is used to enhance the performance on functional representations with a large basis dimension. This method provides an estimation strategy to determine the penalty parameter and the optimal number of components. Our independent component approach is applied to real EEG data to estimate genuine brain potentials from a contaminated signal. As a result, it is possible to control high-frequency remnants of neural origin overlapping artifactual sources to optimize their removal from the signal. An R package implementing our methods is available at CRAN.

Low frequency independent components: Internal neuromarkers linking cortical LFPs to behavior

“…To separate the different generators that compose the LFP signal, we employed independent component analysis (ICA), which has been extensively used and validated in EEG 54 , 55 and in LFP signals. 15 , 50 , 56 , 57 ICA is based on the following three presumptions (i) the data recorded by the electrode array are a spatially stable mixture of the activities of temporally independent brain sources (also noise sources), (ii) the mixture of potentials arising from different parts of the brain is linear at the electrodes, and the propagation delays from the sources to the electrodes are insignificant, and (iii) the number of sources is not greater than the number of electrodes.…”

Novel whitening approaches in functional settings

“…Interestingly, the projection of $$$ X\in \mathbb{H} $$$ on to span $$$ \left(\left\{{\gamma}_j\right\}\right),\kern1em j\in \left\{1,\kern.5em \dots, \kern0.5em q\right\} $$$, that is, $$$ {X}^{(q)}={P}_{\gamma}^{(q)}X $$$, where $$$ q $$$ is fixed to minimize $$$ E{\left\Vert X-{X}^{(q)}\right\Vert}^2 $$$, provides a natural mechanism of regularization by the second‐order structure of the variable. This regularization procedure combined with an additional roughness penalty based on the $$$ d $$$‐order derivative on $$$ {\gamma}_j $$$ yields to a bi‐smoothed approximation to whitening (Vidal et al, 2021), which in turn can enhance posterior analyses of low‐dimensional structures in high‐dimensional settings. Other concomitant methods to solve ill‐posed problems for functional data are reported in Kraus and Stefanucci (2019).…”

“…The motivation behind this article is to discuss the optimization and the use of whitening. The importance of this transformation lies at the core of invariant coordinate selection (Ilmonen et al, 2012; Tyler et al, 2009) and independent component analysis (Nordhausen & Oja, 2018) as well as their functional counterparts (Archimbaud et al, 2022; Vidal et al, 2021; Virta et al, 2020). Whitening enforces statistical independence and allows certain rotational freedom to enhance the estimation of components with non‐Gaussian kurtosis or skewness, which are commonly encountered in economic, neuroscientific and biomechanical data.…”

Basis expansion approaches for functional analysis of variance with repeated measures

“… 2020 ; Vidal et al. 2021 ), canonical correlation (Krzysko and Waszak 2013 ; Keser and Kocakoç 2015 ), clustering (Jacques and Preda 2014a ; Fortuna et al. 2018 ; Sharp and Browne 2021 ; Alvarez-Esteban and Garcia-Escudero 2021 ) and discriminant analysis (Araki et al.…”