Arash Golibagh Mahyari

A Tensor Decomposition-Based Approach for Detecting Dynamic Network States From EEG

Functional connectivity (FC), defined as the statistical dependency between distinct brain regions, has been an important tool in understanding cognitive brain processes. Most of the current works in FC have focused on the assumption of temporally stationary networks. However, recent empirical work indicates that FC is dynamic due to cognitive functions. Goal: The purpose of this paper is to understand the dynamics of FC for understanding the formation and dissolution of networks of the brain. Method: In this paper, we introduce a two-step approach to characterize the dynamics of functional connectivity networks (FCNs) by first identifying change points at which the network connectivity across subjects shows significant changes and then summarizing the FCNs between consecutive change points. The proposed approach is based on a tensor representation of FCNs across time and subjects yielding a four-mode tensor. The change points are identified using a subspace distance measure on low-rank approximations to the tensor at each time point. The network summarization is then obtained through tensor-matrix projections across the subject and time modes. Results: The proposed framework is applied to electroencephalogram (EEG) data collected during a cognitive control task. The detected change-points are consistent with a priori known ERN interval. The results show significant connectivities in medial-frontal regions which are consistent with widely observed ERN amplitude measures. Conclusion: The tensor-based method outperforms conventional matrix-based methods such as singular value decomposition in terms of both change-point detection and state summarization. Significance: The proposed tensor-based method captures the topological structure of FCNs which provides more accurate change-point-detection and state summarization.

Two-dimensional SVD for event detection in dynamic functional brain networks

In recent years, there has been a growing interest in analyzing functional connectivity networks estimated from neuroimaging technologies using graph theory. Previous studies of the functional brain networks have focused on extracting static or time-independent networks to describe the long-term behavior of brain activity. In this paper, we propose a dynamic functional brain network tracking and summarization approach to describe the time-varying evolution of connectivity patterns in functional brain activity. The proposed approach is based on two-dimensional SVD of the three-mode tensor representation of dynamic graphs. First, the event intervals are identified based on the change in the reconstruction error in the lower dimensional space and then the activity in the event intervals are summarized. The proposed method is evaluated for characterizing time-varying network dynamics from event-related potential (ERP) data indexing the well-known error-related negativity (ERN) component related to cognitive control.

Hierarchical distributed compressive sensing for simultaneous sparse approximation and common component extraction

Abstract Simultaneous sparse approximation is a generalization of the standard sparse approximation, for simultaneously representing a set of signals using a common sparsity model. Distributed compressive sensing (DCS) framework has utilized simultaneous sparse approximation for generalizing compressive sensing to multiple signals. DCS finds the sparse representation of multiple correlated signals from compressive measurements using the common + innovation signal model. However, DCS is limited for joint recovery of a large number of signals since it requires large memory and computational time. In this paper, we propose a new hierarchical algorithm to implement the joint sparse recovery part of DCS more efficiently. The proposed approach is based on partitioning the input set and hierarchically solving for the sparse common component across these partitions. The numerical evaluation of the proposed method shows the decrease in computational time over DCS with an increase in reconstruction error. The proposed algorithm is evaluated for two different applications. In the first application, the proposed method is applied to video background extraction problem, where the background corresponds to the common sparse activity across frames. In the second application, a common network structure is extracted from dynamic functional brain connectivity networks.

A Tucker decomposition based approach for topographic functional connectivity state summarization

The brain reconfigures itself continuously in response to different external stimuli. Advances in noninvasive brain activity recording has made it possible to gain insight into the functional brain activity over time. The functional connectivity has been mostly characterized as a static network through linear and nonlinear measures of statistical dependency. However, recent work indicates that functional connectivity is dynamic and this dynamic reconfiguration of connections accounts for various cognitive functions. The goal of this study is to provide a concise summarization of the quasi-stationary functional connectivity network state within a time interval across subjects. We propose to consider the functional connectivity networks constructed by bivariate phase synchrony measure as tensors and use Tucker decomposition to obtain a low-rank approximation to summarize the network. The significant connections within a given network state are obtained through significance testing. Finally, the proposed framework is applied to multichannel electroencephalogram (EEG) data from a study of error processing in the brain to investigate the connectivity patterns during error and correct responses.

Fourier transform for signals on dynamic graphs

Signal processing on graphs offers a new way of analyzing multivariate signals. The different relationships among the sources generating the multivariate signals can be captured by weighted graphs where the nodes are the signal sources and the edges correspond to the relationships between these signals. Classical signal processing concepts need to be adapted to signals on graphs. In this paper, we propose a graph Fourier transform for signals on dynamic graphs, where the relationships vary over time. The proposed transform is evaluated on both simulated and real dynamic social networks with signal defined on its nodes.

Structured dictionary learning for sparse common component and innovation model

Event-related potentials (ERP)s are electrophysiological responses that are commonly used for detecting the brain response to external stimuli. In this paper, we propose to use the sparse common component and innovations model (SCCI) to extract ERPs from multiple EEG signals recorded across closely located electrodes. This model finds the sparse representation of the common component of the signals and their innovation components with respect to pre-determined common and innovation dictionaries, where the common component refer to an event captured by adjacent electrodes such as ERPs. However, different stimuli may produce different responses and predetermining the dictionary may not always be optimal. Therefore, we introduce a structured dictionary learning method to simultaneously learn the two dictionaries from training data. The proposed method is applied to a study of error monitoring where two different types of brain responses are elicited corresponding to the decision made by the subject. The learned dictionaries can discriminate between the response types and extract the ERP corresponding to the two responses.

Multiple subject analysis of functional brain network communities through co-regularized spectral clustering

In recent years, the human brain has been characterized as a complex network composed of segregated modules linked by short path lengths. In order to understand the organization of the network, it is important to determine these modules underlying the functional brain networks. However, the study of these modules is confounded by the fact that most neurophysiological studies consist of data collected from multiple subjects. Typically, this problem is addressed by either averaging the data across subjects which omits the variability across subjects or using consensus clustering methods which treats all subjects equally irrespective of outliers in the data. In this paper, we adapt a recently introduced co-regularized multiview spectral clustering approach to address these problems. The proposed framework is applied to EEG data collected during a study of error-related negativity (ERN) to better understand the functional networks involved in cognitive control and to compare between the network structure between error and correct responses.

Multi-scale anomaly detection in complex dynamic networks

Graphs arise naturally in a wide range of disciplines and applications since they capture the association between entities of a complex network. Recently, there has been an interest in time-evolving or dynamic graphs which can capture the change in the relational information across time. One important problem of interest in dynamic graphs is to detect the changes or anomalies in graph structure across time and identify the edges that conribute to these anomalies. In this paper, we propose a multi-scale analysis of dynamic graphs based on the Wavelet Packet Decomposition to separate the transient edge activity from the stationary background activity. Modeling the wavelet packet coefficients using a Gaussian Mixture Model, we derive a Neyman Pearson detector to identify anomalous edges both in time and space. Experiments illustrate the effectiveness of the method for both simulated and real dynamic networks.