Jason A. Palmer

Independent EEG sources are dipolar

Independent component analysis (ICA) and blind source separation (BSS) methods are increasingly used to separate individual brain and non-brain source signals mixed by volume conduction in electroencephalographic (EEG) and other electrophysiological recordings. We compared results of decomposing thirteen 71-channel human scalp EEG datasets by 22 ICA and BSS algorithms, assessing the pairwise mutual information (PMI) in scalp channel pairs, the remaining PMI in component pairs, the overall mutual information reduction (MIR) effected by each decomposition, and decomposition ‘dipolarity’ defined as the number of component scalp maps matching the projection of a single equivalent dipole with less than a given residual variance. The least well-performing algorithm was principal component analysis (PCA); best performing were AMICA and other likelihood/mutual information based ICA methods. Though these and other commonly-used decomposition methods returned many similar components, across 18 ICA/BSS algorithms mean dipolarity varied linearly with both MIR and with PMI remaining between the resulting component time courses, a result compatible with an interpretation of many maximally independent EEG components as being volume-conducted projections of partially-synchronous local cortical field activity within single compact cortical domains. To encourage further method comparisons, the data and software used to prepare the results have been made available (http://sccn.ucsd.edu/wiki/BSSComparison).

Subset selection in noise based on diversity measure minimization

We develop robust methods for subset selection based on the minimization of diversity measures. A Bayesian framework is used to account for noise in the data and a maximum a posteriori (MAP) estimation procedure leads to an iterative procedure which is a regularized version of the focal underdetermined system solver (FOCUSS) algorithm. The convergence of the regularized FOCUSS algorithm is established and it is shown that the stable fixed points of the algorithm are sparse. We investigate three different criteria for choosing the regularization parameter: quality of fit; sparsity criterion; L-curve. The L-curve method, as applied to the problem of subset selection, is found not to be robust, and we propose a novel modified L-curve procedure that solves this problem. Each of the regularized FOCUSS algorithms is evaluated through simulation of a detection problem, and the results are compared with those obtained using a sequential forward selection algorithm termed orthogonal matching pursuit (OMP). In each case, the regularized FOCUSS algorithm is shown to be superior to the OMP in noisy environments.

Newton method for the ICA mixture model

We derive an asymptotic Newton algorithm for quasi-maximum likelihood estimation of the ICA mixture model, using the ordinary gradient and Hessian. The probabilistic mixture framework yields an algorithm that can accommodate non-stationary environments and arbitrary source densities. We prove asymptotic stability when the source models match the true sources. An example application to EEC segmentation is given.

Super-Gaussian mixture source model for ICA

We propose an extension of the mixture of factor (or independent component) analyzers model to include strongly super-gaussian mixture source densities. This allows greater economy in representation of densities with (multiple) peaked modes or heavy tails than using several Gaussians to represent these features. We derive an EM algorithm to find the maximum likelihood estimate of the model, and show that it converges globally to a local optimum of the actual non-gaussian mixture model without needing any approximations. This extends considerably the class of source densities that can be used in exact estimation, and shows that in a sense super-gaussian densities are as natural as Gaussian densities. We also derive an adaptive Generalized Gaussian algorithm that learns the shape parameters of Generalized Gaussian mixture components. Experiments verify the validity of the algorithm.

Genetic Overlap between Evoked Frontocentral Theta-Band Phase Variability, Reaction Time Variability, and Attention-Deficit/Hyperactivity Disorder Symptoms in a Twin Study

BACKGROUND Electrophysiological and hemodynamic activity is altered in attention-deficit/hyperactivity disorder (ADHD) during tasks requiring cognitive control. Frontal midline theta oscillations are a cortical correlate of cognitive control influencing behavioral outcomes including reaction times. Reaction time variability (RTV) is consistently increased in ADHD and is known to share genetic effects with the disorder. The etiological relationship between the cognitive control system, RTV, and ADHD is unknown. In a sample of twins selected for ADHD and matched control subjects, we aimed to quantify the strength of the phenotypic, genetic, and environmental relationships between event-related midline theta oscillations, RTV, and ADHD. METHODS Our sample included 134 participants aged 12 to 15 years: 67 twin pairs (34 monozygotic; 33 dizygotic) with concordance or discordance for ADHD symptomatology assessed at 8, 10, and 12 years of age. Our main outcome measures were frontal midline theta activity, derived from both channel and source decomposed electroencephalographic data, and behavioral performance on a response-choice arrow flanker task known to elicit theta activity. RESULTS Variability in stimulus event-related theta phase from frontal midline cortex is strongly related to both RTV and ADHD, both phenotypically and genetically. CONCLUSIONS This is the first finding to confirm the genetic link between the frontal midline cognitive control system and ADHD and the first to identify a genetically related neurophysiological marker of RTV in ADHD. Variability in the timing of the theta signal in ADHD may be part of a dysfunctional brain network that impairs regulation of task-relevant responses in the disorder.

Modeling and estimation of dependent subspaces with non-radially symmetric and skewed densities

We extend the Gaussian scale mixture model of dependent subspace source densities to include non-radially symmetric densities using Generalized Gaussian random variables linked by a common variance. We also introduce the modeling of skew in source densities and subspaces using a generalization of the Normal Variance-Mean mixture model. We give closed form expressions for subspace likelihoods and parameter updates in the EM algorithm.

Electrocortical source imaging of intracranial EEG data in epilepsy

Here we report first results of numerical methods for modeling the dynamic structure and evolution of epileptic seizure activity in an intracranial subdural electrode recording from a patient with partial refractory epilepsy. A 16-min dataset containing two seizures was decomposed using up to five competing adaptive mixture independent component analysis (AMICA) models. Multiple models modeled early or late ictal, or pre- or post-ictal periods in the data, respectively. To localize sources, a realistic Boundary Element Method (BEM) head model was constructed for the patient with custom open skull and plastic (non-conductive) electrode holder features. Source localization was performed using Sparse Bayesian Learning (SBL) on a dictionary of overlapping multi-scale cortical patches constructed from 80,130 dipoles in gray matter perpendicular to the cortical surface. Remaining mutual information among seizure-model AMICA components was dominated by two dependent component subspaces with largely contiguous source domains localized to superior frontal gyrus and precen-tral gyrus; these accounted for most of the ictal activity. Similar though much weaker dependent subspaces were also revealed in pre-ictal data by the associated AMICA model. Electrocortical source imaging appears promising both for clinical epilepsy research and for basic cognitive neuroscience research using volunteer patients who must undergo invasive monitoring for medical purposes.

Strong sub-and super-gaussianity

We introduce the terms strong sub- and super-Gaussianity to refer to the previously introduced class of densities log-concave is x2 and log-convex in x2 respectively. We derive relationships among the various definitions of suband super-Gaussianity, and show that strong sub- and super-Gaussianity are related to the score function being star-shaped upward or downward with respect to the origin. We illustrate the definitions and results by extending a theorem of Benveniste, Goursat, and Ruget on uniqueness of separating local optima in ICA.

Contrast functions for independent subspace analysis

We consider the Independent Subspace Analysis problem from the point of view of contrast functions, showing that contrast functions are able to partially solve the ISA problem. That is, basic ICA can solve the ISA problem up to within-subspace separation/analysis. We define sub- and super-Gaussian subspaces and extend to ISA a previous result on freedom of ICA from local optima. We also consider new types of dependent densities that satisfy or violate the entropy power inequality (EPI) condition.

A complex cross-spectral distribution model using Normal Variance Mean Mixtures

We propose a model for the density of cross-spectral coefficients using Normal Variance Mean Mixtures. We show that this model density generalizes the corresponding marginal density of the Complex Wishart distribution for the cross-spectral density. The Maximum Likelihood estimate of parameters in the distribution is derived, and examples are given from alpha brain wave sources in separated EEG data.