Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models

Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network’s low-dimensional structure, and the nodes that participate in it, using any null model. We use generative models to estimate the expected eigenvalue distribution under a specified null model, and then detect where the data network’s eigenspectra exceed the estimated bounds. On synthetic networks, this spectral estimation approach cleanly detects transitions between random and community structure, recovers the number and membership of communities, and removes noise nodes. On real networks spectral estimation finds either a significant fraction of noise nodes or no departure from a null model, in stark contrast to traditional community detection methods. Across all analyses, we find the choice of null model can strongly alter conclusions about the presence of network structure. Our spectral estimation approach is therefore a promising basis for detecting low-dimensional structure in real-world networks, or lack thereof.

Graph Modification Approaches

This chapter contains some of the most recent techniques and algorithms on social network anonymisation. The authors start with the random perturbation algorithms like the UMGA algorithm and constrained perturbation algorithms like the fast k-degree anonymization (FKDA) algorithm. Then they move to the anonymisation technique, noise nodes addition, and present an algorithm based upon this approach. Next, the authors move on to α-anonymization, (α, k) anonymity, (α, l) diversity, and recursive (α, c, l) diversity anonymisation algorithms, which are generalisations in that order.

214 Using Interictal Multivariate Granger Causality to Detect Epileptogenic Hubs

INTRODUCTION Surgical localization of epileptogenic networks requires significant intensive-care stays and facilitation of seizures for visual inspection. Multivariate Granger Causality (MVGC) provides a method of calculating the directional influence from each node to every other node during interictal data before seizures are facilitated after implantation of electrodes. MVGC is an efficient method of detecting biological coupling and has been shown to be robust against noise. Nodes identified as influential by MVGC have recently been shown to correlate with predicted seizure zones. METHODS Electrocorticography was examined and analyzed for five patients undergoing seizure localization surgery. Used ECOG channels were sampled at greater than 1.5 KHz for all patients. Model estimation was performed, and MVGC was used to calculate patterns of directional coupling over 100 second time windows. MVGC was performed on entire stays for two patients and on subsampled data for 3 patients. Coupling was also examined in the frequency domain to establish frequency basis of information exchange. Comparisons were made after blinded analysis was complete with seizure nodes identified by epileptologists. RESULTS >Five patients were included with more than 12 weeks of recorded data. MVGC adjacency matrices from interictal data over time from each patient revealed significant dominance by few nodes (average 1.8). Coupling changed little over time with highly accurate reconstructions after an average of 184 minutes when compared to the average matrix over the entire stay. On comparison to seizure onset nodes determined by epileptologist, the analysis found concordance 92.1% of the time with high significance compared to randomly selected channels (P < 0.00001). CONCLUSION MVGC is a method of detecting directional coupling in ECOG recordings. Previous and current work suggests that influential nodes during interictal data may predict epileptogenic hubs. Data collection may only require a few hours to reproduce the predicted influential nodes, potentially dramatically reducing the required length of stay.

Preventing Identity Disclosure in Social Networks Using Intersected Node

Social networks like Facebook, Twitter, Pinterest etc. provide data of its users to the demanding organizations to better comprehend the quality of their potential clients. Publishing confidential data of social network users in its raw form raises several privacy and security concerns. Recently, some anonymization techniques have been developed to address these issues. In this paper, a technique to prevent identity disclosure through structure attacks has been proposed which not only prevents identity disclosure but also preserves utility of data published by online social networks. Algorithms have been developed by using noise nodes/edges with the consideration of introducing minimum change in the original graphical structure of social networks. The authors' work is unique in the sense that previous works are based on edge editing only but their proposed work protects against structure attacks using mutual nodes in the social network and the effectiveness of the proposed technique has been proved using APL (Average Path Length) and information loss as parameters.

Jammer Location-Oriented Noise Node Elimination Method for MHWN

It is crucial to find the location of the radio jammer for implementing anti-jamming methods and thus resuming the communication and management of MHWN. Nevertheless, due to the influence of environmental factors and the mutual interference of normal nodes, several unaffected nodes are unable to accurately identify whether they are affected by jammer and thus become noise nodes in the jammer location-oriented process, thereby influencing the precision of jamming localization algorithm and causing remarkable error. In this paper, an algorithm is put forward to eliminate noise nodes based on the Mean of Squared Distance among the nodes. Through calculating the Mean of Squared Distance of each node, the authors can find out the noise nodes and remove them. Simulation results in different jamming localization algorithms verify the correctness and effectiveness of the proposed algorithm. Analysis results reveal that the performance of the proposed algorithm is more prominent when the incidence of noise node is small.