Yu-Teng Chang

Frontal information flow and connectivity in psychopathy

Despite accumulating evidence of structural deficits in individuals with psychopathy, especially in frontal regions, our understanding of systems-level disturbances in cortical networks remains limited. We applied novel graph theory-based methods to assess information flow and connectivity based on cortical thickness measures in 55 individuals with psychopathy and 47 normal controls. Compared with controls, the psychopathy group showed significantly altered interregional connectivity patterns. Furthermore, bilateral superior frontal cortices in the frontal network were identified as information flow control hubs in the psychopathy group in contrast to bilateral inferior frontal and medial orbitofrontal cortices as network hubs of the controls. Frontal information flow and connectivity may have a significant role in the neuropathology of psychopathy.

To cut or not to cut? Assessing the modular structure of brain networks

A wealth of methods has been developed to identify natural divisions of brain networks into groups or modules, with one of the most prominent being modularity. Compared with the popularity of methods to detect community structure, only a few methods exist to statistically control for spurious modules, relying almost exclusively on resampling techniques. It is well known that even random networks can exhibit high modularity because of incidental concentration of edges, even though they have no underlying organizational structure. Consequently, interpretation of community structure is confounded by the lack of principled and computationally tractable approaches to statistically control for spurious modules. In this paper we show that the modularity of random networks follows a transformed version of the Tracy-Widom distribution, providing for the first time a link between module detection and random matrix theory. We compute parametric formulas for the distribution of modularity for random networks as a function of network size and edge variance, and show that we can efficiently control for false positives in brain and other real-world networks.

Partitioning directed graphs based on modularity and information flow

Although models of the behavior of individual neurons and synapses are now well established, understanding the way in which they cooperate in large ensembles remains a major scientific challenge. We present two novel graph theory methods to study cortical interactions and image the highly organized structure of large scale networks. First, we present a new method to partition directed graphs into modules, based on modularity and an expected network conditioned on the in- and out-degrees of all nodes. We also propose a method to segment graphs based on information flow. These methods are combined to study the community structure of brain networks and information flow within the modules.

Statistically optimal graph partition method based on modularity

Graph theory provides a formal framework to investigate the functional and structural connectome of the brain. We extend previous work on modularity-based graph partitioning methods that are able to detect network community structures. We estimate the conditional expected network, provide exact analytical solutions for a Gaussian random network, and also demonstrate that this network is the best unbiased linear estimator even when the Gaussian assumption is violated. We use the conditional expected network to partition graphs, and demonstrate its performance in simulations, a real network dataset, and a structural brain connectivity network.

Statistically optimal modular partitioning of directed graphs

Network models can be used to represent interacting subsystems in the brain or other biological systems. These subsystems can be identified by partitioning a graph representation of the network into highly connected modules. In this paper we describe a modularity-based partitioning method based on a Gaussian model of a directed graph. Using the degrees of each node, we first compute the conditional expected value of the connection weights. The resulting adjacency matrix forms a null model for the network which does not favor any particular partition. By comparing this null model to the true adjacency graph, we can perform a statistically optimal partitioning that maximizes modularity. Similarly to other modularity-based partitioning methods, the solution is found using spectral matrix decomposition. The process can be iterated to find multiple subgraphs. We demonstrate this approach through simulations and application to standard biological and other network data.

Assessing statistical significance when partitioning large-scale brain networks

Multivariate analysis of structural and functional brain imaging data can be used to produce network models of interaction or similarity between different brain structures. Graph partitioning methods can then be used to identify distinct subnetworks that may provide insight into the organization of the human brain. Although several efficient partitioning algorithms have been proposed, and their properties studied thoroughly, there has been limited work addressing the statistical significance of the resulting partitions. We present a new method to estimate the statistical significance of a network structure based on modularity. We derive a numerical approximation of the distribution of modularity on random graphs, and use this distribution to calculate a threshold that controls the type I error rate in partitioning graphs. We demonstrate the technique in application to brain subnetworks identified from diffusion-based fiber tracking data and from resting state fMRI data.

Modularity gradients: Measuring the contribution of edges to the community structure of a brain network

Modularity measures the quality of a particular division of a brain network, and it tends to have high values for networks with strong community structure. In this paper we show that the derivative of modularity with respect to each edge in a network quantifies the contribution of the edge to the global modular structure of the network. We derive analytical forms for the derivative of modularity and investigate its properties. Our approach focuses on the significance of edges on modularity and deviates from standard node-centric network measures, such as hub analysis.

Parametric distributions for assessing significance in modular partitions of brain networks

Brain networks are often explored with graph theoretical approaches, and community structures identified using modularity-based partitions. Despite the popularity of these methods, the significance of the obtained subnetworks is largely unaddressed in the literature. We present two parametric methods to assess the statistical significance of network partitions, and therefore control against spurious subnetworks that may arise in random graphs, rather than self-organized brain networks. We evaluate these methods with simulated data and resting state fMRI data.

Of the largest eigenvalue for modularity-based partitioning

Despite the popularity and broad range of spectral clustering algorithms, there is little work addressing the statistical significance of clustering results. Spectral clustering uses the eigenvalues of matrices, such as the Laplacian graph or the adjacency matrix minus a null model, to partition a network. Even though the distribution of the largest eigenvalue for these matrices is not known, random matrix theory provides analytical formulas for a family of matrices called Gaussian random ensembles. We demonstrate that the Tracy-Widom mapping of the largest eigenvalue of Gaussian random ensembles can be modified to predict the distribution of the largest eigenvalue of matrices used for modularity-based spectral clustering. Using this finding we derive formulas that control the type I error rate on modularity-based partitions.

Multi-view network module detection

Fundamental to the identification of the architecture and organization of complex systems is the detection of modules, also called communities or clusters, through the use of graph partition methods. In this paper, we extend one of the most popular graph partition methods, modularity, to jointly preserve the structure of multiple networks using the multi-view technique. Under the assumption that the same modular structure is shared by all network realizations, we show that the multi-view approach is robust against scaling, noise and outliers. In addition, it can overcome some resolution limitations of the traditional modularity-based method. We demonstrate the performance of the combined modularity-multiview method in simulations and experimental data from a 191-subject functional brain network.