Covariance, correlation matrix, and the multiscale community structure of networks

Characterization of multiple topological scales in multiplex networks through supra-Laplacian eigengaps

Multilayer networks have been the subject of intense research during the past few years, as they represent better the interdependent nature of many real-world systems. Here, we address the question of describing the three different structural phases in which a multiplex network might exist. We show that each phase can be characterized by the presence of gaps in the spectrum of the supra-Laplacian of the multiplex network. We therefore unveil the existence of different topological scales in the system, whose relation characterizes each phase. Moreover, by capitalizing on the coarse-grained representation that is given in terms of quotient graphs, we explain the mechanisms that produce those gaps as well as their dynamical consequences.

Selectively-informed particle swarm optimization

Particle swarm optimization (PSO) is a nature-inspired algorithm that has shown outstanding performance in solving many realistic problems. In the original PSO and most of its variants all particles are treated equally, overlooking the impact of structural heterogeneity on individual behavior. Here we employ complex networks to represent the population structure of swarms and propose a selectively-informed PSO (SIPSO), in which the particles choose different learning strategies based on their connections: a densely-connected hub particle gets full information from all of its neighbors while a non-hub particle with few connections can only follow a single yet best-performed neighbor. Extensive numerical experiments on widely-used benchmark functions show that our SIPSO algorithm remarkably outperforms the PSO and its existing variants in success rate, solution quality, and convergence speed. We also explore the evolution process from a microscopic point of view, leading to the discovery of different roles that the particles play in optimization. The hub particles guide the optimization process towards correct directions while the non-hub particles maintain the necessary population diversity, resulting in the optimum overall performance of SIPSO. These findings deepen our understanding of swarm intelligence and may shed light on the underlying mechanism of information exchange in natural swarm and flocking behaviors.

Active semi-supervised community detection based on must-link and cannot-link constraints

Community structure detection is of great importance because it can help in discovering the relationship between the function and the topology structure of a network. Many community detection algorithms have been proposed, but how to incorporate the prior knowledge in the detection process remains a challenging problem. In this paper, we propose a semi-supervised community detection algorithm, which makes full utilization of the must-link and cannot-link constraints to guide the process of community detection and thereby extracts high-quality community structures from networks. To acquire the high-quality must-link and cannot-link constraints, we also propose a semi-supervised component generation algorithm based on active learning, which actively selects nodes with maximum utility for the proposed semi-supervised community detection algorithm step by step, and then generates the must-link and cannot-link constraints by accessing a noiseless oracle. Extensive experiments were carried out, and the experimental results show that the introduction of active learning into the problem of community detection makes a success. Our proposed method can extract high-quality community structures from networks, and significantly outperforms other comparison methods.

A community detection algorithm based on topology potential and spectral clustering

Community detection is of great value for complex networks in understanding their inherent law and predicting their behavior. Spectral clustering algorithms have been successfully applied in community detection. This kind of methods has two inadequacies: one is that the input matrixes they used cannot provide sufficient structural information for community detection and the other is that they cannot necessarily derive the proper community number from the ladder distribution of eigenvector elements. In order to solve these problems, this paper puts forward a novel community detection algorithm based on topology potential and spectral clustering. The new algorithm constructs the normalized Laplacian matrix with nodes' topology potential, which contains rich structural information of the network. In addition, the new algorithm can automatically get the optimal community number from the local maximum potential nodes. Experiments results showed that the new algorithm gave excellent performance on artificial networks and real world networks and outperforms other community detection methods.

SEMI-SUPERVISED LEARNING OF K-NEAREST NEIGHBORS USING A NEAREST-NEIGHBOR SELF-CONTAINED CRITERION IN FOR MOBILE-AWARE SERVICE

We propose a new K-nearest neighbor (KNN) algorithm based on a nearest-neighbor self-contained criterion (NNscKNN) by utilizing the unlabeled data information. Our algorithm incorporates other discriminant information to train KNN classifier. This new KNN scheme is also applied in a community detection algorithm for mobile-aware service: First, as the edges of networks, the social relation between mobile nodes is quantified with social network theory; second, we would construct the mobile nodes optimal path tree and calculate the similarity index of adjacent nodes; finally, the community dispersion is defined to evaluate the clustering results and measure the quality of community structure. Promising experiments on benchmarks demonstrate the effectiveness of our approach for recognition and detection tasks.

The network structure of human personality according to the NEO-PI-R: matching network community structure to factor structure

Introduction

Human personality is described preferentially in terms of factors (dimensions) found using factor analysis. An alternative and highly related method is network analysis, which may have several advantages over factor analytic methods.

Aim

To directly compare the ability of network community detection (NCD) and principal component factor analysis (PCA) to examine modularity in multidimensional datasets such as the neuroticism-extraversion-openness personality inventory revised (NEO-PI-R).

Methods

434 healthy subjects were tested on the NEO-PI-R. PCA was performed to extract factor structures (FS) of the current dataset using both item scores and facet scores. Correlational network graphs were constructed from univariate correlation matrices of interactions between both items and facets. These networks were pruned in a link-by-link fashion while calculating the network community structure (NCS) of each resulting network using the Wakita Tsurumi clustering algorithm. NCSs were matched against FS and networks of best matches were kept for further analysis.

Results

At facet level, NCS showed a best match (96.2%) with a ‘confirmatory’ 5-FS. At item level, NCS showed a best match (80%) with the standard 5-FS and involved a total of 6 network clusters. Lesser matches were found with ‘confirmatory’ 5-FS and ‘exploratory’ 6-FS of the current dataset. Network analysis did not identify facets as a separate level of organization in between items and clusters. A small-world network structure was found in both item- and facet level networks.

Conclusion

We present the first optimized network graph of personality traits according to the NEO-PI-R: a ‘Personality Web’. Such a web may represent the possible routes that subjects can take during personality development. NCD outperforms PCA by producing plausible modularity at item level in non-standard datasets, and can identify the key roles of individual items and clusters in the network.

Degree-strength correlation reveals anomalous trading behavior

Manipulation is an important issue for both developed and emerging stock markets. Many efforts have been made to detect manipulation in stock markets. However, it is still an open problem to identify the fraudulent traders, especially when they collude with each other. In this paper, we focus on the problem of identifying the anomalous traders using the transaction data of eight manipulated stocks and forty-four non-manipulated stocks during a one-year period. By analyzing the trading networks of stocks, we find that the trading networks of manipulated stocks exhibit significantly higher degree-strength correlation than the trading networks of non-manipulated stocks and the randomized trading networks. We further propose a method to detect anomalous traders of manipulated stocks based on statistical significance analysis of degree-strength correlation. Experimental results demonstrate that our method is effective at distinguishing the manipulated stocks from non-manipulated ones. Our method outperforms the traditional weight-threshold method at identifying the anomalous traders in manipulated stocks. More importantly, our method is difficult to be fooled by colluded traders.

Overlapping community detection via network dynamics

The modular structure of a network is closely related to the dynamics toward clustering. In this paper, a method for community detection is proposed via the clustering dynamics of a network. The initial phases of the nodes in the network are given randomly, and then they evolve according to a set of dedicatedly designed differential equations. The phases of the nodes are naturally separated into several clusters after a period of evolution, and each cluster corresponds to a community in the network. For the networks with overlapping communities, the phases of the overlapping nodes will evolve to the interspace of the two communities. The proposed method is illustrated with applications to both synthetically generated and real-world complex networks.

Exploring the structural regularities in networks

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically, we propose a general statistical model to describe network structure. In this model, a group is viewed as a hidden or unobserved quantity and it is learned by fitting the observed network data using the expectation-maximization algorithm. Compared with existing models, the most prominent strength of our model is the high flexibility. This strength enables it to possess the advantages of existing models and to overcome their shortcomings in a unified way. As a result, not only can broad types of structure be detected without prior knowledge of the type of intrinsic regularities existing in the target network, but also the type of identified structure can be directly learned from the network. Moreover, by differentiating outgoing edges from incoming edges, our model can detect several types of structural regularities beyond competing models. Tests on a number of real world and artificial networks demonstrate that our model outperforms the state-of-the-art model in shedding light on the structural regularities of networks, including the overlapping community structure, multipartite structure, and several other types of structure, which are beyond the capability of existing models.

The interaction between multiplex community networks

Multiplex community networks, consisting of several different types of simplex networks and interconnected among them, are ubiquitous in the real world. In this paper, we carry out a quantitative discussion on the interaction among these diverse simplex networks. First, we define two measures, mutual-path-strength and proximity-node-density, based on twoplex community networks and then propose an impact-strength-index (ISI) to describe the influence of a simplex network on the other one. Finally, we apply the measure ISI to make an explanation for the challenge system of social relations from the viewpoint of network theory. Numerical simulations show that the measure ISI can describe the interaction between multiplex community networks perfectly.