Directed information for complex network analysis from multivariate time series
Complex networks, ranging from gene regulatory networks in biology to social networks in sociology, have received growing attention from the scientific community. The analysis of complex networks employs techniques from graph theory, machine learning and signal processing. In recent years, complex n...
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01.01.2012
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| Abstract | Complex networks, ranging from gene regulatory networks in biology to social networks in sociology, have received growing attention from the scientific community. The analysis of complex networks employs techniques from graph theory, machine learning and signal processing. In recent years, complex network analysis tools have been applied to neuroscience and neuroimaging studies to have a better understanding of the human brain. In this thesis, we focus on inferring and analyzing the complex functional brain networks underlying multichannel electroencephalogram (EEG) recordings. Understanding this complex network requires the development of a measure to quantify the relationship between multivariate time series, algorithms to reconstruct the network based on the pairwise relationships, and identification of functional modules within the network. Functional and effective connectivity are two widely studied approaches to quantify the connectivity between two recordings. Unlike functional connectivity which only quantifies the statistical dependencies between two processes by measures such as cross correlation, phase synchrony, and mutual information (MI), effective connectivity quantifies the influence one node exerts on another node. Directed information (DI) measure is one of the approaches that has been recently proposed to capture the causal relationships between two time series. Two major challenges remain with the application of DI to multivariate data, which include the computational complexity of computing DI with increasing signal length and the accuracy of estimation from limited realizations of the data. Expressions that can simplify the computation of the original definition of DI while still quantifying the causality relationship are needed. In addition, the advantage of DI over conventionally causality measures such as Granger causality has not been fully investigated. In this thesis, we propose time-lagged directed information and modified directed information to address the issue of computational complexity, and compare the performance of this model free measure with model based measures (e.g. Granger causality) for different realistic signal models. Once the pairwise DI between two random processes is computed, another problem is to infer the underlying structure of the complex network with minimal false positive detection. We propose to use conditional directed information (CDI) proposed by Kramer to address this issue, and introduce the time-lagged conditional directed information and modified conditional directed information to lower the computational complexity of CDI. Three network inference algorithms are presented to infer directed acyclic networks which can quantify the causality and also detect the indirect couplings simultaneously from multivariate data. One last challenge in the study of complex networks, specifically in neuroscience applications, is to identify the functional modules from multichannel, multiple subject recordings. Most research on community detection in this area so far has focused on finding the association matrix based on functional connectivity, instead of effective connectivity, thus not capturing the causality in the network. In addition, in order to find a modular structure that best describes all of the subjects in a group, a group analysis strategy is needed. In this thesis, we propose a multi-subject hierarchical community detection algorithm suitable for a group of weighted and asymmetric (directed) networks representing effective connectivity, and apply the algorithm to multichannel electroencephalogram (EEG) data. |
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| AbstractList | Complex networks, ranging from gene regulatory networks in biology to social networks in sociology, have received growing attention from the scientific community. The analysis of complex networks employs techniques from graph theory, machine learning and signal processing. In recent years, complex network analysis tools have been applied to neuroscience and neuroimaging studies to have a better understanding of the human brain. In this thesis, we focus on inferring and analyzing the complex functional brain networks underlying multichannel electroencephalogram (EEG) recordings. Understanding this complex network requires the development of a measure to quantify the relationship between multivariate time series, algorithms to reconstruct the network based on the pairwise relationships, and identification of functional modules within the network. Functional and effective connectivity are two widely studied approaches to quantify the connectivity between two recordings. Unlike functional connectivity which only quantifies the statistical dependencies between two processes by measures such as cross correlation, phase synchrony, and mutual information (MI), effective connectivity quantifies the influence one node exerts on another node. Directed information (DI) measure is one of the approaches that has been recently proposed to capture the causal relationships between two time series. Two major challenges remain with the application of DI to multivariate data, which include the computational complexity of computing DI with increasing signal length and the accuracy of estimation from limited realizations of the data. Expressions that can simplify the computation of the original definition of DI while still quantifying the causality relationship are needed. In addition, the advantage of DI over conventionally causality measures such as Granger causality has not been fully investigated. In this thesis, we propose time-lagged directed information and modified directed information to address the issue of computational complexity, and compare the performance of this model free measure with model based measures (e.g. Granger causality) for different realistic signal models. Once the pairwise DI between two random processes is computed, another problem is to infer the underlying structure of the complex network with minimal false positive detection. We propose to use conditional directed information (CDI) proposed by Kramer to address this issue, and introduce the time-lagged conditional directed information and modified conditional directed information to lower the computational complexity of CDI. Three network inference algorithms are presented to infer directed acyclic networks which can quantify the causality and also detect the indirect couplings simultaneously from multivariate data. One last challenge in the study of complex networks, specifically in neuroscience applications, is to identify the functional modules from multichannel, multiple subject recordings. Most research on community detection in this area so far has focused on finding the association matrix based on functional connectivity, instead of effective connectivity, thus not capturing the causality in the network. In addition, in order to find a modular structure that best describes all of the subjects in a group, a group analysis strategy is needed. In this thesis, we propose a multi-subject hierarchical community detection algorithm suitable for a group of weighted and asymmetric (directed) networks representing effective connectivity, and apply the algorithm to multichannel electroencephalogram (EEG) data. |
| Author | Liu, Ying |
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| Title | Directed information for complex network analysis from multivariate time series |
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