A Multi-Dimensional Functional Principal Components Analysis of EEG Data

Abstract

Summary The electroencephalography (EEG) data created in event-related potential (ERP) experiments have a complex high-dimensional structure. Each stimulus presentation, or trial, generates an ERP waveform which is an instance of functional data. The experiments are made up of sequences of multiple trials, resulting in longitudinal functional data and moreover, responses are recorded at multiple electrodes on the scalp, adding an electrode dimension. Traditional EEG analyses involve multiple simplifications of this structure to increase the signal-to-noise ratio, effectively collapsing the functional and longitudinal components by identifying key features of the ERPs and averaging them across trials. Motivated by an implicit learning paradigm used in autism research in which the functional, longitudinal and electrode components all have critical interpretations, we propose a multidimensional functional principal components analysis (MD-FPCA) technique which does not collapse any of the dimensions of the ERP data. The proposed decomposition is based on separation of the total variation into subject and subunit level variation which are further decomposed in a two-stage functional principal components analysis. The proposed methodology is shown to be useful for modeling longitudinal trends in the ERP functions, leading to novel insights into the learning patterns of children with Autism Spectrum Disorder (ASD) and their typically developing peers as well as comparisons between the two groups. Finite sample properties of MD-FPCA are further studied via extensive simulations.

Inferring Brain Signals Synchronicity From a Sample of EEG Readings

“…A similar conclusion is noted in the higher entropy associated with ASD consensus estimates (1.b and 2.b). This observation echoes some of our previous findings in EEG studies of implicit-learning in ASD and TD children (Hasenstab et al 2015;Hasenstab et al 2016a;Hasenstab et al 2016b).…”

Bayesian Semiparametric Functional Mixed Models for Serially Correlated Functional Data, With Application to Glaucoma Data

“…Most commonly, the functions occur along a grid of time points, which could be called longitudinally correlated functional data , but can also occur over other continuous variables such as IOP for our glaucoma data. There are a number of papers that focus on functional predictor regression (Goldsmith et al, 2012; Gertheiss, Goldsmith, Crainiceanu and Greven, 2013; Kundu et al, 2016; Islam et al, 2016) or estimate multi-level principal components (Greven et al, 2010; Zipunnikov et al, 2011; Chen and Müller, 2012; Li and Guan, 2014; Zipunnikov et al, 2014; Park and Staicu, 2015; Shou et al, 2015; Hasenstab et al, 2017) for serially correlated functions, but these papers do not deal directly with functional response regression, i.e. do not regress the functions on covariates while accounting for this serial correlation in the error structure.…”

Parameter clustering in Bayesian functional principal component analysis of neuroscientific data

“…1 One of the advantages of fPCA is that it can be conveniently represented as a hierarchical mixed model in the Bayesian setting, with the joint posterior distribution of the fPC scores being the main target of inference. 3 There has been a growing interest in applying FDA to neuroscientific data (see, among others, Viviani et al, 4 Tian et al, 5 and Hasenstab et al 6 ). Often, in the FDA literature, underlying random curves are assumed to be independent and their correlation is ignored if believed to be mild.…”