Local Network Features Research Articles

Network heterogeneity based on <i>K</i>-order structure entropy

Structure entropy can evaluate the heterogeneity of complex networks, but traditional structure entropy has deficiencies in comprehensively reflecting the global and local network features. In this paper, we define a new structure entropy based on the number of the <i>K</i>-order neighbor nodes which refer to those nodes which a node can reach within <i>K</i> steps. It can be supposed that the more <i>K</i>-order neighbors a node has, the more important role the node plays in the network structure. Combining the formula of Shannon entropy, the <i>K</i>-order structure entropy can be defined and figured out to explain the differences among the relative importance among nodes. Meanwhile, the new structure entropy can describe the network heterogeneity from the following three aspects. The first aspect is the change tendency of structure entropy with the value of <i>K</i>. The second aspect is the structure entropy under a maximum influence scale <i>K</i>. The last aspect is the minimum value of the <i>K</i>-order structure entropy. The simulation compares the heterogeneities of five classic networks from the above three aspects, and the result shows that the heterogeneity strengthens in the from-weak-to -strong sequence:regular network, random network, WS (Watts-Strogatz) small-world network, BA (Barabási-Albert) scale-free network and star network. This conclusion is consistent with the previous theoretical research result, but hard to obtain from the traditional structure entropy. It is remarkable that the <i>K</i>-order structure entropy can better evaluate the heterogeneity of WS small-world networks and suggests that the greater small-world coefficients a network has, the stronger heterogeneity the network has. Besides, the <i>K</i>-order structure entropy can fully reflect the heterogeneity variation of star networks with network size, and reasonably explain the heterogeneity of regular networks with additional isolated nodes. It suggests that when i additional isolated nodes are added to a regular network with <i>n</i> nodes, the new network has weaker heterogeneity than the old one, but has stronger heterogeneity than the regular network with <i>n</i>+i nodes. Finally, the validity of the <i>K</i>-order structure entropy is further confirmed by simulations for the western power grid of the United States. Based on the minimum value of the <i>K</i>-order structure entropy, the heterogeneity of the western power grid is the closest to that of WS small-world networks.

Node importance based on the weighted <i>K</i>-order propagation number algorithm

The measurement of node importance is significant for analyzing a network structure. To comprehensively reflect the global and local network features, in this paper we abstract the propagating process of epidemic diseases based on the network topology structure, and then respectively sets each node as an infection source. After a certain dissemination time <i>K</i>, the number of infected nodes in the network is defined as the <i>K</i>-order propagation number, and the weighted sum of <i>K</i>-order propagation numbers under different values of <i>K</i> is taken as the important index of nodes. The simulation experiments of Watts-Strogatz small-world networks and a dolphin network show that the weighted <i>K</i>-order propagation number algorithm is more effective than the traditional method in evaluating the importance of nodes. For the Watts-Strogatz small-world networks, it can reflect the influence of long-distance connections on information transmission in detail. For the dolphin network, the weighted <i>K</i>-order propagation number algorithm significantly raises the profile of those nodes which play a key role in the information communication between different dolphin communities. In addition, in this paper we use a deliberate attacking method to analyze the western power grid of the United States, the road transportation network of the Chicago region, the co-authorship network in network science and the axonal tracts’ network between neurons of mouse. According to the specific order of the node importance from high to low, network nodes are attacked in turn, that is, all edges of the attacked nodes are removed. The analysis results of network parameters such as the network efficiency and the node number of the maximum sub-graph changing with the attacking times show that comparing with other evaluation indices of node importance such as degree, Ren method, Chen method, eigenvector method, Katz index, PageRank, CI method and <i>K</i>-shell, the weighted <i>K</i>-order propagation number algorithm focuses much on destroying the major structure, and all of the above four networks will break down if only a small number of important nodes are attacked. For example, after attacking only 100 nodes, the network efficiency of the western power grid of the United States is down by 90%, and after attacking 200 nodes, the network scale of the maximum sub-graph is nearly 3% of the original network.

The statistical physics of real-world networks

In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation, scale invariance, emergence of mixed distributions and ensemble non-equivalence, that display unconventional features on heterogeneous networks. At the same time, thanks to their deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models for networks reproducing some features of real-world systems, but otherwise as random as possible. We review here the statistical physics approach and the various null models for complex networks, focusing in particular on the analytic frameworks reproducing the local network features. We then show how these models have been used to detect statistically significant and predictive structural patterns in real-world networks, as well as to reconstruct the network structure in case of incomplete information. We further survey the statistical physics models that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, as well as the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes.

New Keypoint Matching Method Using Local Convolutional Features for Power Transmission Line Icing Monitoring.

Power transmission line icing (PTLI) problems, which cause tremendous damage to the power grids, has drawn much attention. Existing three-dimensional measurement methods based on binocular stereo vision was recently introduced to measure the ice thickness in PTLI, but failed to meet requirements of practical applications due to inefficient keypoint matching in the complex PTLI scene. In this paper, a new keypoint matching method is proposed based on the local multi-layer convolutional neural network (CNN) features, termed Local Convolutional Features (LCFs). LCFs are deployed to extract more discriminative features than the conventional CNNs. Particularly in LCFs, a multi-layer features fusion scheme is exploited to boost the matching performance. Together with a location constraint method, the correspondence of neighboring keypoints is further refined. Our approach achieves 1.5%, 5.3%, 13.1%, 27.3% improvement in the average matching precision compared with SIFT, SURF, ORB and MatchNet on the public Middlebury dataset, and the measurement accuracy of ice thickness can reach 90.9% compared with manual measurement on the collected PTLI dataset.

Local convolutional features and metric learning for SAR image registration

The conventional synthetic aperture radar (SAR) image registration focuses on designing diverse hand-crafted features and distance metrics. It is still challenging to obtain accurate feature correspondence when influenced by speckle noise and geometric distortion. This paper proposes local convolutional neural network (CNN) features based method to solve the keypoint matching problem, whose contributions are threefold. (1) a feature descriptor based on local convolutional features of image patches (LCFs-P) is deployed to extract more discriminative features than the conventional CNNs. (2) A new feature correspondence scheme based on metric learning is proposed to boost the feature matching performance. (3) A local geometric similarity method is employed to remove the mismatches of the tentative matches. The experimental results on the real SAR dataset and Middlebury dataset demonstrate that the proposed model outperforms the existing state-of-the-art methods in terms of matching accuracy and efficiency.

Classify epileptic EEG signals using weighted complex networks based community structure detection

Abstract Background Epilepsy is a brain disorder that is mainly diagnosed by neurologists based on electroencephalogram (EEG) recordings. Epileptic EEG signals are recorded as multichannel signals. A reliable technique for analysing multi-channel EEG signals is in urgent demand for the treatment and diagnosis of patients who have epilepsy and other brain disorders. Method In this paper, each single EEG channel is partitioned into four segments, with each segment is further divided into small clusters. A set of statistical features are extracted from each cluster. As a result, a vector of all the features from each EEG single channel is obtained. The resulting features vector is then mapped into an undirected weighted network. The modularity of the networks is found to be the best to detect epileptic seizures in EEG signals. Other local and global network features, including clustering coefficients, average degree and closeness centrality, are also extracted and studied. All the network attributes are ranked based on their potential to detect abnormalities in EEG signals. Results Eight pairs of combinations of EEG signals are classified by the proposed method using four well known classifiers: a least support vector machine, k -means, Naive Bayes, and K -nearest. The proposed method achieved an average of 98%, 96.5%, 99%, rand 0.012, respectively, for its accuracy, sensitivity, specificity and the false positive rate. Comparisons were made using several existing epileptic seizures detection methods using the same datasets. The obtained results showed that the proposed method was efficient in detecting epileptic seizures in EEG signals.

Changes in brain-behavior relationships following a 3-month pilot cognitive intervention program for adults with traumatic brain injury.

Facilitating functional recovery following brain injury is a key goal of neurorehabilitation. Direct, objective measures of changes in the brain are critical to understanding how and when meaningful changes occur, however, assessing neuroplasticity using brain based results remains a significant challenge. Little is known about the underlying changes in functional brain networks that correlate with cognitive outcomes in traumatic brain injury (TBI). The purpose of this pilot study was to assess the feasibility of an intensive three month cognitive intervention program in individuals with chronic TBI and to evaluate the effects of this intervention on brain-behavioral relationships. We used tools from graph theory to evaluate changes in global and local brain network features prior to and following cognitive intervention. Network metrics were calculated from resting state electroencephalographic (EEG) recordings from 10 adult participants with mild to severe brain injury and 11 age and gender matched healthy controls. Local graph metrics showed hyper-connectivity in the right inferior frontal gyrus and hypo-connectivity in the left inferior frontal gyrus in the TBI group at baseline in comparison with the control group. Following the intervention, there was a statistically significant increase in the composite cognitive score in the TBI participants and a statistically significant decrease in functional connectivity in the right inferior frontal gyrus. In addition, there was evidence of changes in the brain-behavior relationships following intervention. The results from this pilot study provide preliminary evidence for functional network reorganization that parallels cognitive improvements after cognitive rehabilitation in individuals with chronic TBI.

Heter-LP: A heterogeneous label propagation algorithm and its application in drug repositioning

Drug repositioning offers an effective solution to drug discovery, saving both time and resources by finding new indications for existing drugs. Typically, a drug takes effect via its protein targets in the cell. As a result, it is necessary for drug development studies to conduct an investigation into the interrelationships of drugs, protein targets, and diseases. Although previous studies have made a strong case for the effectiveness of integrative network-based methods for predicting these interrelationships, little progress has been achieved in this regard within drug repositioning research. Moreover, the interactions of new drugs and targets (lacking any known targets and drugs, respectively) cannot be accurately predicted by most established methods.In this paper, we propose a novel semi-supervised heterogeneous label propagation algorithm named Heter-LP, which applies both local and global network features for data integration. To predict drug-target, disease-target, and drug-disease associations, we use information about drugs, diseases, and targets as collected from multiple sources at different levels. Our algorithm integrates these various types of data into a heterogeneous network and implements a label propagation algorithm to find new interactions. Statistical analyses of 10-fold cross-validation results and experimental analyses support the effectiveness of the proposed algorithm.

Machine-Learning Classifier for Patients with Major Depressive Disorder: Multifeature Approach Based on a High-Order Minimum Spanning Tree Functional Brain Network.

High-order functional connectivity networks are rich in time information that can reflect dynamic changes in functional connectivity between brain regions. Accordingly, such networks are widely used to classify brain diseases. However, traditional methods for processing high-order functional connectivity networks generally include the clustering method, which reduces data dimensionality. As a result, such networks cannot be effectively interpreted in the context of neurology. Additionally, due to the large scale of high-order functional connectivity networks, it can be computationally very expensive to use complex network or graph theory to calculate certain topological properties. Here, we propose a novel method of generating a high-order minimum spanning tree functional connectivity network. This method increases the neurological significance of the high-order functional connectivity network, reduces network computing consumption, and produces a network scale that is conducive to subsequent network analysis. To ensure the quality of the topological information in the network structure, we used frequent subgraph mining technology to capture the discriminative subnetworks as features and combined this with quantifiable local network features. Then we applied a multikernel learning technique to the corresponding selected features to obtain the final classification results. We evaluated our proposed method using a data set containing 38 patients with major depressive disorder and 28 healthy controls. The experimental results showed a classification accuracy of up to 97.54%.

Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

Descriptive neural network analyses have provided important insights into the organization of structural and functional networks in the human brain. However, these analyses have limitations for inter-subject or between-group comparisons in which network sizes and edge densities may differ, such as in studies on neurodevelopment or brain diseases. Furthermore, descriptive neural network analyses lack an appropriate generic null model and a unifying framework. These issues may be solved with an alternative framework based on a Bayesian generative modeling approach, i.e. Bayesian exponential random graph modeling (ERGM), which explains an observed network by the joint contribution of local network structures or features (for which we chose neurobiologically meaningful constructs such as connectedness, local clustering or global efficiency). We aimed to identify how these local network structures (or features) are evolving across the life-span, and how sensitive these features are to random and targeted lesions. To that aim we applied Bayesian exponential random graph modeling on structural networks derived from whole-brain diffusion tensor imaging-based tractography of 382 healthy adult subjects (age range: 20.2–86.2years), with and without lesion simulations. Networks were successfully generated from four local network structures that resulted in excellent goodness-of-fit, i.e. measures of connectedness, local clustering, global efficiency and intrahemispheric connectivity. We found that local structures (i.e. connectedness, local clustering and global efficiency), which give rise to the global network topology, were stable even after lesion simulations across the lifespan, in contrast to overall descriptive network changes – e.g. lower network density and higher clustering – during aging, and despite clear effects of hub damage on network topologies. Our study demonstrates the potential of Bayesian generative modeling to characterize the underlying network structures that drive the brain's global network topology at different developmental stages and/or under pathological conditions.

The structure of internal job mobility and organizational wage inequality

The movement of people among jobs within an organization reflects a process of relational position-taking—a contest among individuals for valued resources. The structure of this mobility offers clues regarding the relational dynamics associated with position-taking and how these processes might vary across low and high inequality organizations. We explore these issues using data on intra-organizational mobility networks from 7347 workers in 428 positions in 11 distribution centers from a national grocery store chain. Exponential random graph models are used to identify the local network features that characterize each organization’s pattern of job mobility. This approach is then supplemented with meta-regression that examines the extent to which those network features are associated with organizational inequality (the wage gap between supervisors and non-supervisors). Organizational inequality is unrelated to the presence of purely structural mobility features (density, reciprocity, or transitivity), but instead is characterized by the confluence of mobility structure and positional hierarchy. The findings demonstrate that workers have fewer mobility pathways into high wage jobs in high inequality organizations than in low inequality organizations.

The racial disparities in STI in the U.S.: Concurrency, STI prevalence, and heterogeneity in partner selection

BackgroundThere is a large and persistent racial disparity in STI in the U.S. which has placed non-Hispanic-Blacks at disproportionately high risk. We tested a hypothesis that both individual-level risk factors (partner number, anal sex, condom use) and local-network features (concurrency and assortative mixing by race) combine to account for the association between race and chlamydia status. MethodsData from the Longitudinal Survey of Adolescent Health Wave III were used. Chlamydia status was determined using biomarkers. Individual-level risk behaviors were self-reported. Network location variables for concurrency and assortative mixing were imputed using egocentrically sample data on sexual partnerships. ResultsAfter controlling for demographic attributes including age, sex, marital status, education and health care access there remained a strong association between race and chlamydia status (OR=5.23, 95% CI [3.83–7.15], p<.001 for Non-Hispanic Blacks with Non-Hispanic Whites as the reference category). The inclusion of individual-level risk factors did not alter the association between race and chlamydia (OR=5.23 for Non-Hispanic Blacks). The inclusion of concurrency and assortative mixing by race substantially reduced the association between race and chlamydia status (OR=1.87, 95% CI [0.89–3.91] p>.05 for Non-Hispanic Blacks).

The emergence of roles in large-scale networks of communication

Communication through social media mediates coordination and information diffusion across a range of social settings. However, online networks are large and complex, and their analysis requires new methods to summarize their structure and identify nodes holding relevant positions. We propose a method that generalizes the sociological theory of brokerage, originally devised on the basis of local transitivity and paths of length two, to make it applicable to larger, more complex structures. Our method makes use of the modular structure of networks to define brokerage at the local and global levels. We test the method with two different data sets. The findings show that our approach is better at capturing role differences than alternative approaches that only consider local or global network features.

Connectome and Maturation Profiles of the Developing Mouse Brain Using Diffusion Tensor Imaging

This paper presents a comprehensive effort to establish a structural mouse connectome using diffusion tensor magnetic resonance imaging coupled with connectivity analysis tools. This work lays the foundation for imaging-based structural connectomics of the mouse brain, potentially facilitating a whole-brain network analysis to quantify brain changes in connectivity during development, as well as deviations from it related to genetic effects. A connectomic trajectory of maturation during postnatal ages 2-80 days is presented in the C57BL/6J mouse strain, using a whole-brain connectivity analysis, followed by investigations based on local and global network features. The global network measures of density, global efficiency, and modularity demonstrated a nonlinear relationship with age. The regional network metrics, namely degree and local efficiency, displayed a differential change in the major subcortical structures such as the thalamus and hippocampus, and cortical regions such as visual and motor cortex. Finally, the connectomes were used to derive an index of "brain connectivity index," which demonstrated a high correlation (r = 0.95) with the chronological age, indicating that brain connectivity is a good marker of normal age progression, hence valuable in detecting subtle deviations from normality caused by genetic, environmental, or pharmacological manipulations.

The Emergence of Roles in Large-Scale Networks of Communication

Communication through social media mediates coordination and information diffusion across a range of social settings. However, online networks are large and complex, and their analysis requires new methods to summarize their structure and identify nodes holding relevant positions. We propose a method that generalizes the sociological theory of brokerage, originally devised on the basis of local transitivity and paths of length two, to make it applicable to larger, more complex structures. Our method makes use of the modular structure of networks to define brokerage at the local and global levels. We test the method with two different data sets. The findings show that our approach is better at capturing role differences than alternative approaches that only consider local or global network features.

Boosted network classifiers for local feature selection.

Like all models, network feature selection models require that assumptions be made on the size and structure of the desired features. The most common assumption is sparsity, where only a small section of the entire network is thought to produce a specific phenomenon. The sparsity assumption is enforced through regularized models, such as the lasso. However, assuming sparsity may be inappropriate for many real-world networks, which possess highly correlated modules. In this paper, we illustrate two novel optimization strategies, namely, boosted expectation propagation (BEP) and boosted message passing (BMP), which directly use the network structure to estimate the parameters of a network classifier. BEP and BMP are ensemble methods that seek to optimize classification performance by combining individual models built upon local network features. Neither BEP nor BMP assumes a sparse solution, but instead they seek a weighted average of all network features where the weights are used to emphasize all features that are useful for classification. In this paper, we compare BEP and BMP with network-regularized logistic regression models on simulated and real biological networks. The results show that, where highly correlated network structure exists, assuming sparsity adversely effects the accuracy and feature selection power of the network classifier.

Quantitative network features of the basal ganglia and connectome based population simulations

Quantitative network features of the basal ganglia and connectome based population simulations

Exponential Random Graph Modeling for Complex Brain Networks

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks.

Automatic Network Fingerprinting through Single-Node Motifs

Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs—a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the new routines are validated in different network-series. Third, we provide an example of how the method can be used to analyse network time-series. In conclusion, we provide a robust method for systematically discovering and classifying characteristic nodes of a network. In contrast to classical motif analysis, our approach can identify individual components (here: nodes) that are specific to a network. Such special nodes, as hubs before, might be found to play critical roles in real-world networks.

Comparing social networks

This paper demonstrates limitations in usefulness of the triad census for studying similarities among local structural properties of social networks. A triad census succinctly summarizes the local structure of a network using the frequencies of sixteen isomorphism classes of triads (sub-graphs of three nodes). The empirical base for this study is a collection of 51 social networks measuring different relational contents (friendship, advice, agonistic encounters, victories in fights, dominance relations, and so on) among a variety of species (humans, chimpanzees, hyenas, monkeys, ponies, cows, and a number of bird species). Results show that, in aggregate, similarities among triad censuses of these empirical networks are largely explained by nodal and dyadic properties – the density of the network and distributions of mutual, asymmetric, and null dyads. These results remind us that the range of possible network-level properties is highly constrained by the size and density of the network and caution should be taken in interpreting higher order structural properties when they are largely explained by local network features.