Time-evolving Networks Research Articles

Statistical methods utilizing structural properties of time-evolving networks for event detection

Statistical methods utilizing structural properties of time-evolving networks for event detection

Optimizing parameter search for community detection in time-evolving networks of complex systems.

Network representations have been effectively employed to analyze complex systems across various areas and applications, leading to the development of network science as a core tool to study systems with multiple components and complex interactions. There is a growing interest in understanding the temporal dynamics of complex networks to decode the underlying dynamic processes through the temporal changes in network structures. Community detection algorithms, which are specialized clustering algorithms, have been instrumental in studying these temporal changes. They work by grouping nodes into communities based on the structure and intensity of network connections over time, aiming to maximize the modularity of the network partition. However, the performance of these algorithms is highly influenced by the selection of resolution parameters of the modularity function used, which dictate the scale of the represented network, in both size of communities and the temporal resolution of the dynamic structure. The selection of these parameters has often been subjective and reliant on the characteristics of the data used to create the network. Here, we introduce a method to objectively determine the values of the resolution parameters based on the elements of self-organization and scale-invariance. We propose two key approaches: (1) minimization of biases in spatial scale network characterization and (2) maximization of scale-freeness in temporal network reconfigurations. We demonstrate the effectiveness of these approaches using benchmark network structures as well as real-world datasets. To implement our method, we also provide an automated parameter selection software package that can be applied to a wide range of complex systems.

Predicting Learning Interactions in Social Learning Networks: A Deep Learning Enabled Approach

We consider the problem of predicting link formation in Social Learning Networks (SLN), a type of social network that forms when people learn from one another through structured interactions. While link prediction has been studied for general types of social networks, the evolution of SLNs over their lifetimes coupled with their dependence on which topics are being discussed presents new challenges for this type of network. To address these challenges, we develop a series of autonomous link prediction methodologies that utilize spatial and time-evolving network architectures to pass network state between space and time periods, and that models over three types of SLN features updated in each period: neighborhood-based (e.g., resource allocation), path-based (e.g., shortest path), and post-based (e.g., topic similarity). Through evaluation on six real-world datasets from Massive Open Online Course (MOOC) discussion forums and from Purdue University, we find that our method obtains substantial improvements over Bayesian models, linear classifiers, and graph neural networks, with AUCs typically above 0.91 and reaching 0.99 depending on the dataset. Our feature importance analysis shows that while neighborhood and path-based features contribute the most to the results, post-based features add additional information that may not always be relevant for link prediction. The code and four of the datasets used in this work are available at https://github.com/Jess-jpg-txt/sln-learning.

A framework for reconstructing transmission networks in infectious diseases

In this paper, we propose a general framework for the reconstruction of the underlying cross-regional transmission network contributing to the spread of an infectious disease. We employ an autoregressive model that allows to decompose the mean number of infections into three components that describe: intra-locality infections, inter-locality infections, and infections from other sources such as travelers arriving to a country from abroad. This model is commonly used in the identification of spatiotemporal patterns in seasonal infectious diseases and thus in forecasting infection counts. However, our contribution lies in identifying the inter-locality term as a time-evolving network, and rather than using the model for forecasting, we focus on the network properties without any assumption on seasonality or recurrence of the disease. The topology of the network is then studied to get insight into the disease dynamics. Building on this, and particularly on the centrality of the nodes of the identified network, a strategy for intervention and disease control is devised.

Network science approach to predict the yield strength of metals containing soft particles and pores

Local fluctuations in particle size and spatial distributions can substantially affect the yield strength of metals containing soft particles and/or porosities. The phenomenon can be studied via computational homogenization techniques, which, however, can be highly computationally demanding when large representative volume elements are needed. A more efficient approach to model the plastic deformation that controls the yield strength of metals containing pores has recently been proposed by the author and co-workers. The key idea is to treat the material as a network rather than as a continuum. In fact, plastic deformation in porous metals occurs via the formation of shear bands connecting the pores, and it can thus be modelled as a time-evolving network where the nodes represent the pores and the links represent the shear bands. So far, the applicability of this new approach has only been tested against 2D synthetic microstructures. The present work takes it a step further by applying the approach to real spheroidal graphite iron. Based on strain data collected in-situ via digital volume correlation, it is shown that the new network approach can explain the spatial variations of the plastic deformation that arise from local variations of the particle distribution throughout a tensile specimen.

Temporal Graphs and Temporal Network Characteristics for Bio-Inspired Networks during Optimization

Temporal network analysis and time evolution of network characteristics are powerful tools in describing the changing topology of dynamic networks. This paper uses such approaches to better visualize and provide analytical measures for the changes in performance that we observed in Voronoi-type spatial coverage, particularly for the example of time-evolving networks with a changing number of wireless sensors being deployed. Specifically, our analysis focuses on the role different combinations of impenetrable obstacles and environmental noise play in connectivity and overall network structure. It is shown how the use of (i) temporal network graphs, and (ii) network centrality and regularity measures illustrate the differences between various options developed for the balancing act of energy and time efficiency in network coverage. Last, we compare the outcome of these measures with the less abstract classification variables, such as percent area covered and cumulative distance traveled.

Statistical Consistency for Change Point Detection and Community Estimation in Time-Evolving Dynamic Networks

Suppose a time sequence of networks is observed. It is known that the probabilistic behaviors of the networks do not change over time, except at a few time points. These time points are usually called change points, whose number and locations are unknown. This paper proposes a method for automatically estimating such change points and the community structures of the networks. The proposed method invokes the minimum description length principle to derive a model selection criterion, where the best estimates are defined as its minimizer. It is shown that this selection criterion yields consistent estimates for the change points as well as the community structures. For practical minimization of the selection criterion, a bottom-up search algorithm that combines the EM-algorithm with variational approximation is developed. The promising empirical properties of the proposed method are illustrated via a sequence of numerical experiments and applications to some real datasets. To the best of the authors’ knowledge, this method is one of the earliest that provides consistent estimates in the context of change point detection for time-evolving networks.

Dynamic Structural Role Node Embedding for User Modeling in Evolving Networks

Complex user behavior, especially in settings such as social media, can be organized as time-evolving networks. Through network embedding, we can extract general-purpose vector representations of these dynamic networks which allow us to analyze them without extensive feature engineering. Prior work has shown how to generate network embeddings while preserving the structural role proximity of nodes. These methods, however, cannot capture the temporal evolution of the structural identity of the nodes in dynamic networks. Other works, on the other hand, have focused on learning microscopic dynamic embeddings. Though these methods can learn node representations over dynamic networks, these representations capture the local context of nodes and do not learn the structural roles of nodes. In this article, we propose a novel method for learning structural node embeddings in discrete-time dynamic networks. Our method, called HR2vec , tracks historical topology information in dynamic networks to learn dynamic structural role embeddings. Through experiments on synthetic and real-world temporal datasets, we show that our method outperforms other well-known methods in tasks where structural equivalence and historical information both play important roles. HR2vec can be used to model dynamic user behavior in any networked setting where users can be represented as nodes. Additionally, we propose a novel method (called network fingerprinting) that uses HR2vec embeddings for modeling whole (or partial) time-evolving networks. We showcase our network fingerprinting method on synthetic and real-world networks. Specifically, we demonstrate how our method can be used for detecting foreign-backed information operations on Twitter.

Statistical mechanical analysis for unweighted and weighted stock market networks

Financial markets are time-evolving complex systems containing different financial entities, such as banks, corporations and institutions that interact through transactions and respond to external economic and political events. They can be conveniently represented as a network structure. In this paper, we analyse the unweighted and weighted market networks from a statistical mechanical perspective. In particular, we propose a novel thermodynamic analogy to characterise the dynamic structural properties of time-evolving networks. The intricate pattern of edge connections in the network is modelled by using a heat bath analogy in which particles occupy the energy states according to the Boltzmann distribution. According to this analogy the occupation of the energy states is determined by the temperature of the heat bath, and the spectrum of energy states of the network is determined by the number of nodes and edges. For unweighted networks, the binary representation of the elements in the adjacency matrix can be modelled as a statistical ensemble, using the corresponding partition function to compute thermodynamic network characterisations. For weighted networks, on the other hand, the derived thermodynamic quantities together with their distribution of fluctuations identify the salient structure in the network evolution. We conduct experiments on time-evolving stock exchanges using data for the S&P500 Index Stock Exchanges over the past decade. The thermodynamic characterisations provide an excellent framework to identify epochs in which there is significant variance in network structure during financial crises induced by economic and political events.

RecTen: A Recursive Hierarchical Low Rank Tensor Factorization Method to Discover Hierarchical Patterns from Multi-modal Data

How can we expand the tensor decomposition to reveal a hierarchical structure of the multi-modal data in a self-adaptive way? Current tensor decomposition provides only a single layer of clusters. We argue that with the abundance of multimodal data and time-evolving networks nowadays, the ability to identify emerging hierarchies is important. To this effect, we propose RecTen, a multi-modal hierarchical clustering approach based on tensor decomposition. Our approach enables us to: (a) recursively decompose clusters identified in the previous step, and (b) identify the right conditions for terminating this process. In the absence of a well-established benchmark, we evaluate our approach with synthetic and five real datasets. First, we test the sensitivity of the performance to different scenarios and parameters. Second, we apply RecTen on four online forums and a dataset that represents user interaction on GitHub. This analysis identifies meaningful and interesting behaviors, which further increases our confidence in the usefulness of our approach. For example, we identify some real events like ransomware outbreaks (55 users, 86 threads, December 2015, February 2016), the emergence of a black-market of decryption tools (34 users, 12 threads, February 2016), and romance scamming (82 users, 172 threads, March 2018). To maximize the impact of our work, we intend to: (a) develop a usable tool, (b) make the tool and our datasets publicly available. However, RecTen is a hierarchical clustering approach that can be used to take the pulse of large multimodal data and let the data reveal its own hidden structures.

Biological Networks across Scales-The Theoretical and Empirical Foundations for Time-Varying Complex Networks that Connect Structure and Function across Levels of Biological Organization.

Many biological systems across scales of size and complexity exhibit a time-varying complex network structure that emerges and self-organizes as a result of interactions with the environment. Network interactions optimize some intrinsic cost functions that are unknown and involve for example energy efficiency, robustness, resilience, and frailty. A wide range of networks exist in biology, from gene regulatory networks important for organismal development, protein interaction networks that govern physiology and metabolism, and neural networks that store and convey information to networks of microbes that form microbiomes within hosts, animal contact networks that underlie social systems, and networks of populations on the landscape connected by migration. Increasing availability of extensive (big) data is amplifying our ability to quantify biological networks. Similarly, theoretical methods that describe network structure and dynamics are being developed. Beyond static networks representing snapshots of biological systems, collections of longitudinal data series can help either at defining and characterizing network dynamics over time or analyzing the dynamics constrained to networked architectures. Moreover, due to interactions with the environment and other biological systems, a biological network may not be fully observable. Also, subnetworks may emerge and disappear as a result of the need for the biological system to cope with for example invaders or new information flows. The confluence of these developments renders tractable the question of how the structure of biological networks predicts and controls network dynamics. In particular, there may be structural features that result in homeostatic networks with specific higher-order statistics (e.g., multifractal spectrum), which maintain stability over time through robustness and/or resilience to perturbation. Alternative, plastic networks may respond to perturbation by (adaptive to catastrophic) shifts in structure. Here, we explore the opportunity for discovering universal laws connecting the structure of biological networks with their function, positioning them on the spectrum of time-evolving network structure, that is, dynamics of networks, from highly stable to exquisitely sensitive to perturbation. If such general laws exist, they could transform our ability to predict the response of biological systems to perturbations-an increasingly urgent priority in the face of anthropogenic changes to the environment that affect life across the gamut of organizational scales.

WINTENDED: WINdowed TENsor decomposition for Densification Event Detection in time-evolving networks

Densification events in time-evolving networks refer to instants in which the network density, that is, the number of edges, is substantially larger than in the remaining. These events can occur at a global level, involving the majority of the nodes in the network, or at a local level involving only a subset of nodes.While global densification events affect the overall structure of the network, the same does not hold in local densification events, which may remain undetectable by the existing detection methods. In order to address this issue, we propose WINdowed TENsor decomposition for Densification Event Detection (WINTENDED) for the detection and characterization of both global and local densification events. Our method combines a sliding window decomposition with statistical tools to capture the local dynamics of the network and automatically find the irregular behaviours. According to our experimental evaluation, WINTENDED is able to spot global densification events at least as accurately as its competitors, while also being able to find local densification events, on the contrary to its competitors.

Thermodynamic motif analysis for directed stock market networks

In this paper, we present a novel thermodynamically based analysis method for directed networks, and in particular for time-evolving networks in the finance domain. Based on an analogy with a dilute gas in statistical mechanics, we develop a partition function for a network composed of directed motifs. The method relies on the decomposition of directed networks into a series of frequently occurring graphlets, or motifs. According to the connection between a directed network and the dilute gas, the network motifs have the same topological structure as the low-order interactions between particles in the gas. This means that we can use the so-called cluster expansion from statistical mechanics to develop a partition function for the motif decomposition. In prior work, we have reported a detailed analysis of the cluster expansion for the case of undirected graphs, and showed how the resulting motif entropy can be used to analyse time evolving networks [1]. In this paper we extend this work to the case of directed graphs to compute thermodynamic quantities including energy, entropy and temperature for the directed network. The three thermodynamic quantities constitute the thermodynamic framework for the analysis of directed network evolution. We apply our thermodynamic framework to the financial and biological domains to represent real world complex systems as time-varying directed networks. Experimental results successfully demonstrate the effectiveness of the thermodynamic framework in representing the evolution of directed network structure and anomalous event detection.

Network broadcast analysis and control of turbulent flows

Abstract

Integrating old and new complexity measures toward automated seizure detection from long-term video EEG recordings

SummaryAutomated seizure detection in long-term video-EEG recordings is far from being integrated into common clinical practice. Here, we leverage classical and state-of-the-art complexity measures to robustly and automatically detect seizures from scalp recordings. Brain activity is scored through eight features, encompassing traditional time domain and novel measures of recurrence. A binary classification algorithm tailored to treat unbalanced dataset is used to determine whether a time window is ictal or non-ictal from its features. The application of the algorithm on a cohort of ten adult patients with focal refractory epilepsy indicates sensitivity, specificity, and accuracy of 90%, along with a true alarm rate of 95% and less than four false alarms per day. The proposed approach emphasizes ictal patterns against noisy background without the need of data preprocessing. Finally, we benchmark our approach against previous studies on two publicly available datasets, demonstrating the good performance of our algorithm.

IncNSA: Detecting communities incrementally from time-evolving networks based on node similarity

Many real-world systems can be abstracted as networks. As those systems always change dynamically in nature, the corresponding networks also evolve over time in general, and detecting communities from such time-evolving networks has become a critical task. In this paper, we propose an incremental detection method, which can stably detect high-quality community structures from time-evolving networks. When the network evolves from the previous snapshot to the current one, the proposed method only considers the community affiliations of partial nodes efficiently, which are either newborn nodes or some active nodes from the previous snapshot. Thus, the first phase of our method is determining active nodes that should be reassigned due to the change of their community affiliations in the evolution. Then, we construct subgraphs for these nodes to obtain the preliminary communities in the second phase. Finally, the final result can be obtained through optimizing the primary communities in the third phase. To test its performance, extensive experiments are conducted on both some synthetic networks and some real-world dynamic networks, the results show that our method can detect satisfactory community structure from each of snapshot graphs efficiently and steadily, and outperforms the competitors significantly.

Extra-adaptive robust online subspace tracker for anomaly detection from streaming networks

Anomaly detection in time-evolving networks has many applications, for instance, traffic analysis in transportation networks and intrusion detection in computer networks. One group of popular methods for anomaly detection from evolving networks are robust online subspace trackers. However, these methods suffer from problem of insensitivity to drastic changes in the evolving subspace. In order to solve this problem, we propose a new robust online subspace and anomaly tracker, which is more adaptive and robust against sudden drastic changes in the subspace. More accurate estimation of low rank and sparse components by this tracker leads to more accurate anomaly detection. We evaluate the accuracy of our method with real-world dynamic network data sets with varying sparsity levels. The result is promising and our method outperforms the state-of-the-art.

Link prediction of time-evolving network based on node ranking

Many real-world networks belong to the kind that evolves over time. So it is very meaningful and challenging to predict whether the link will occur in the network of future time. In this paper, both time-evolving scale-free (SF) network and real-world dynamic network are taken into consideration first and then two kinds of methods are respectively proposed for link prediction. Different from many existing similarity-based dynamic network link prediction methods, many of which adopt node-pair similarity such as common neighbors (CN), Adamic–Adar (AA), and so on, we measure the similarity between nodes from a new perspective. With further research into node ranking, some eigenvector-based methods, such as PageRank (PR), Cumulative Nomination (CuN) and so on, can compute the values of node importance which can be regarded as the stationary distribution of Markov chain for all nodes iteratively. Therefore, from a statistical point of view, the importance of a node is like the probability of attracting other nodes to connect with it and the derivative value of a node pair is like the probability of attracting each other. These node-ranking-based approaches are very novel in the field of link prediction in that few researches have paid enough attention to them before. In addition, an adaptively time series forecasting method is proposed in this paper, and it uses the historical similarity series to predict the future similarity between each node pair adaptively. Experimental results show that our proposed algorithms can predict the future links not only for the growing SF network but also for the dynamic networks in the real-world.

Open system quantum thermodynamics of time-varying graphs

AbstractIn this article, we present a novel analysis of time-evolving networks, based on a thermodynamic representation of graph structure. We show how to characterize the evolution of time-varying complex networks by relating major structural changes to thermodynamic phase transitions. In particular, we derive expressions for a number of different thermodynamic quantities (specifically energy, entropy and temperature), which we use to describe the evolutionary behaviour of the network system over time. Since in the real world no system is truly closed and interactions with the environment are usually strong, we assume an open nature of the system. We adopt the Schrödinger picture as the dynamical representation of the quantum system over time. First, we compute the network entropy using a recent quantum mechanical representation of graph structure, connecting the graph Laplacian to a density operator. Then, we assume the system evolves according to the Schrödinger representation, but we allow for decoherence due to the interaction with the environment in a model akin to Environment-Induced Decoherence. We simplify the model by separating its dynamics into (a) an unknown time-dependent unitary evolution plus (b) an observation/interaction process, and this is the sole cause of the changes in the eigenvalues of the density matrix of the system. This allows us to obtain a measure of energy exchange with the environment through the estimation of the hidden time-varying Hamiltonian responsible for the unitary part of the evolution. Using the thermodynamic relationship between changes in energy, entropy, pressure and volume, we recover the thermodynamic temperature. We assess the utility of the method on real-world time-varying networks representing complex systems in the financial and biological domains. We also compare and contrast the different characterizations provided by the thermodynamic variables (energy, entropy, temperature and pressure). The study shows that the estimation of the time-varying energy operator strongly characterizes different states of a time-evolving system and successfully detects critical events occurring during network evolution.

Construction And Analysis Of The Time-Evolving Pain-Related Brain Network Using Literature Mining.

PurposeWe aimed to quantitatively investigate how the neuroscience field developed over time in terms of its concept on how pain is represented in the brain and compare the research trends of pain with those of mental disorders through literature mining of accumulated published articles.MethodsThe abstracts and publication years of 137,525 pain-related articles were retrieved from the PubMed database. We defined 22 pain-related brain regions that appeared more than 100 times in the retrieved abstracts. Time-evolving networks of pain-related brain regions were constructed using the co-occurrence frequency. The state-space model was implemented to capture the trend patterns of the pain-related brain regions and the patterns were compared with those of mental disorders.ResultsThe number of pain-related abstracts including brain areas steadily increased; however, the relative frequency of each brain region showed different patterns. According to the chronological patterns of relative frequencies, pain-related brain regions were clustered into three groups: rising, falling, and consistent. The network of pain-related brain regions extended over time from localized regions (mainly including brain stem and diencephalon) to wider cortical/subcortical regions. In the state-space model, the relative frequency trajectory of pain-related brain regions gradually became closer to that of mental disorder-related brain regions.ConclusionTemporal changes of pain-related brain regions in the abstracts indicate that emotional/cognitive aspects of pain have been gradually emphasized. The networks of pain-related brain regions imply perspective changes on pain from the simple percept to the multidimensional experience. Based on the notable occurrence patterns of the cerebellum and motor cortex, we suggest that motor-related areas will be actively explored in pain studies.