Blind source separation using temporal predictability

A measure of temporal predictability is defined and used to separate linear mixtures of signals. Given any set of statistically independent source signals, it is conjectured here that a linear mixture of those signals has the following property: the temporal predictability of any signal mixture is less than (or equal to) that of any of its component source signals. It is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un-mixing matrix that maximizes a measure of temporal predictability for each recovered signal. This matrix is obtained as the solution to a generalized eigenvalue problem; such problems have scaling characteristics of O (N3), where N is the number of signal mixtures. In contrast to independent component analysis, the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals. It is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian, sub-gaussian, and gaussian probability density functions and on mixtures of voices and music

Lagged and instantaneous dynamical influences related to brain structural connectivity

Contemporary neuroimaging methods can shed light on the basis of human neural and cognitive specializations, with important implications for neuroscience and medicine. Different MRI acquisitions provide different brain networks at the macroscale; whilst diffusion-weighted MRI (dMRI) provides a structural connectivity (SC) coincident with the bundles of parallel fibers between brain areas, functional MRI (fMRI) accounts for the variations in the blood-oxygenation-level-dependent T2* signal, providing functional connectivity (FC).Understanding the precise relation between FC and SC, that is, between brain dynamics and structure, is still a challenge for neuroscience. To investigate this problem, we acquired data at rest and built the corresponding SC (with matrix elements corresponding to the fiber number between brain areas) to be compared with FC connectivity matrices obtained by 3 different methods: directed dependencies by an exploratory version of structural equation modeling (eSEM), linear correlations (C) and partial correlations (PC). We also considered the possibility of using lagged correlations in time series; so, we compared a lagged version of eSEM and Granger causality (GC). Our results were two-fold: firstly, eSEM performance in correlating with SC was comparable to those obtained from C and PC, but eSEM (not C nor PC) provides information about directionality of the functional interactions. Second, interactions on a time scale much smaller than the sampling time, captured by instantaneous connectivity methods, are much more related to SC than slow directed influences captured by the lagged analysis. Indeed the performance in correlating with SC was much worse for GC and for the lagged version of eSEM. We expect these results to supply further insights to the interplay between SC and functional patterns, an important issue in the study of brain physiology and function.Comment: Accepted and published in Frontiers in Psychology in its current form. 27 pages, 1 table, 5 figures, 2 suppl. figure

On blind separability based on the temporal predictability method

This letter discusses blind separability based on temporal predictability (Stone, 2001; Xie, He, & Fu, 2005). Our results show that the sources are separable using the temporal predictability method if and only if they have different temporal structures (i.e., autocorrelations). Consequently, the applicability and limitations of the temporal predictability method are clarified. In addition, instead of using generalized eigendecomposition, we suggest using joint approximate diagonalization algorithms to improve the robustness of the method. A new criterion is presented to evaluate the separation results. Numerical simulations are performed to demonstrate the validity of the theoretical results

Mal-Adaptation of Event-Related EEG Responses Preceding Performance Errors

Recent EEG and fMRI evidence suggests that behavioral errors are foreshadowed by systematic changes in brain activity preceding the outcome by seconds. In order to further characterize this type of error precursor activity, we investigated single-trial event-related EEG activity from 70 participants performing a modified Eriksen flanker task, in particular focusing on the trial-by-trial dynamics of a fronto-central independent component that previously has been associated with error and feedback processing. The stimulus-locked peaks in the N2 and P3 latency range in the event-related averages showed expected compatibility and error-related modulations. In addition, a small pre-stimulus negative slow wave was present at erroneous trials. Significant error-preceding activity was found in local stimulus sequences with decreased conflict in the form of less negativity at the N2 latency (310–350 ms) accumulating across five trials before errors; concomitantly response times were speeding across trials. These results illustrate that error-preceding activity in event-related EEG is associated with the performance monitoring system and we conclude that the dynamics of performance monitoring contribute to the generation of error-prone states in addition to the more remote and indirect effects in ongoing activity such as posterior alpha power in EEG and default mode drifts in fMRI