Empirical Temporal Networks Research Articles

Fault Diagnosis Method of Flexible Converter Valve Equipment Based on Ensemble Empirical Mode Decomposition and Temporal Convolutional Networks

The flexible converter valve is a crucial component of the flexible transmission system, and its proper functioning is directly related to the power system's reliability. This study proposes a method for diagnosing faults in flexible converter valve equipment based on ensemble empirical mode decomposition and temporal convolutional networks. The method involves measuring voltage signal data in the power submodule of the flexible converter valve, decomposing and reconstructing the voltage signal using ensemble empirical mode decomposition to extract frequency variation patterns and fault features. Subsequently, a temporal convolutional network is introduced, and a device fault diagnosis model is constructed by learning the evolution law of voltage signals in time series. The experimental results demonstrate that the proposed method has high fault diagnosis accuracy and robustness with an average F1-score of 89.58% and an average area under the curve (AUC) of 94.38%, which are higher than other methods by at least 1.39% and 1.03%.

Robustness of community structure under edge addition.

Communities often represent key structural and functional clusters in networks. To preserve such communities, it is important to understand their robustness under network perturbations. Previous work in community robustness analysis has focused on studying changes in the community structure as a response of edge rewiring and node or edge removal. However, the impact of increasing connectivity on the robustness of communities in networked systems is relatively unexplored. Studying the limits of community robustness under edge addition is crucial to better understanding the cases in which density expands or false edges erroneously appear. In this paper, we analyze the effect of edge addition on community robustness in synthetic and empirical temporal networks. We study two scenarios of edge addition: random and targeted. We use four community detection algorithms, Infomap, Label Propagation, Leiden, and Louvain, and demonstrate the results in community similarity metrics. The experiments on synthetic networks show that communities are more robust when the initial partition is stronger or the edge addition is random, and the experiments on empirical data also indicate that robustness performance can be affected by the community similarity metric. Overall, our results suggest that the communities identified by the different types of community detection algorithms exhibit different levels of robustness, and so the robustness of communities depends strongly on the choice of detection method.

Detecting the driver nodes of temporal networks

Detecting the driver nodes of complex networks has garnered significant attention recently to control complex systems to desired behaviors, where nodes represent system components and edges encode their interactions. Driver nodes, which are directly controlled by external inputs, play a crucial role in controlling all network nodes. While many approaches have been proposed to identify driver nodes of static networks, we still lack an effective algorithm to control ubiquitous temporal networks, where network structures evolve over time. Here we propose an effective online time-accelerated heuristic algorithm (OTaHa) to detect driver nodes of temporal networks. Together with theoretical analysis and numerical simulations on synthetic and empirical temporal networks, we show that OTaHa offers multiple sets of driver nodes, and noticeably outperforms existing methods in terms of accuracy and execution time. We further report that most edges are redundant in controlling temporal networks although the complete instantaneous signal-carrying edges cannot be guaranteed. Moreover, removing edges with high edge betweenness (the number of all-pairs shortest paths passing through the edge) significantly impedes the overall controllability. Our work provides an effective algorithm and paves the way for subsequent explorations on achieving the ultimate control of temporal networks.

Stock index forecasting based on multivariate empirical mode decomposition and temporal convolutional networks

Modeling and forecasting of stock indexes is an important and challenging work in the field of financial research, which is of great significance for investors to reduce risk on investment and improve investment returns. However, the basic data of the stock index includes five indicators, namely, opening price, highest price, lowest price, closing price and trading volume (COHLV), each of which contains some information related to the future trend. And these indicators are affected by different factors such as politics, economy, psychology and so on, so they have nonlinear, high noise and other complex characteristics. These reasons make the existing methods cannot effectively improve the accuracy of stock index forecasting. In order to solve this problem, we propose a hybrid stock index forecasting model named MEMD-TCN, which is based on multivariate empirical mode decomposition (MEMD) and temporal convolutional networks (TCN). The novelty of the proposed model focuses on decomposition of multivariate time series and using only fully convolutional layers to forecast stock index. The proposed model first uses MEMD to decompose the data of COHLV to obtain subsequences of different fluctuation frequencies of each time series, then inputs subsequences of the same frequency into TCN to predict the subsequences of closing price in the next period. Ultimately, the forecasted values for the closing price are obtained by reconstructing the prediction results of all the subsequences of closing price. To evaluate the performance of the proposed MEMD-TCN model, stock index of several countries that can reflect the overall changes of the market are used. The experimental results verify the notable effectiveness and necessity of the decomposition of multivariate time series. Meanwhile, the results demonstrate the significant superiority of the proposed MEMD-TCN model on accuracy and stability.

Randomized Reference Models for Temporal Networks

Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated topologies and dynamics. This makes their analysis particularly challenging. Randomized reference models (RRMs) have emerged as a general and versatile toolbox for studying such systems. Defined as random networks with given features constrained to match those of an input (empirical) network, they may, for example, be used to identify important features of empirical networks and their effects on dynamical processes unfolding in the network. RRMs are typically implemented as procedures that reshuffle an empirical network, making them very generally applicable. However, the effects of most shuffling procedures on network features remain poorly understood, rendering their use nontrivial and susceptible to misinterpretation. Here we propose a unified framework for classifying and understanding microcanonical RRMs (MRRMs) that sample networks with uniform probability. Focusing on temporal networks, we survey applications of MRRMs found in the literature, and we use this framework to build a taxonomy of MRRMs that proposes a canonical naming convention, classifies them, and deduces their effects on a range of important network features. We furthermore show that certain classes of MRRMs may be applied in sequential composition to generate new MRRMs from the existing ones surveyed in this article. We finally provide a tutorial showing how to apply a series of MRRMs to analyze how different network features affect a dynamic process in an empirical temporal network.

Methods for Continuous Blood Pressure Estimation Using Temporal Convolutional Neural Networks and Ensemble Empirical Mode Decomposition

Arterial blood pressure is not only an important index that must be measured in routine physical examination but also a key monitoring parameter of the cardiovascular system in cardiac surgery, drug testing, and intensive care. To improve the measurement accuracy of continuous blood pressure, this paper uses photoplethysmography (PPG) signals to estimate diastolic blood pressure and systolic blood pressure based on ensemble empirical mode decomposition (EEMD) and temporal convolutional network (TCN). In this method, the clean PPG signal is decomposed by EEMD to obtain n-order intrinsic mode functions (IMF), and then the IMF and the original PPG are input into the constructed TCN neural network model, and the results are output. The results show that TCN has better performance than CNN, CNN-LSTM, and CNN-GRU. Using the data added with IMF, the results of the above neural network model are better than those of the model with only PPG as input, in which the systolic blood pressure (SBP) and diastolic blood pressure (DBP) results of EEMD-TCN are −1.55 ± 9.92 mmHg and 0.41 ± 4.86 mmHg. According to the estimation results, DBP meets the requirements of the AAMI standard, BHS evaluates it as Grade A, SD of SBP is close to the standard AAMI, and BHS evaluates it as Grade B.

Dose\u2013response functions and surrogate models for exploring social contagion in the Copenhagen Networks Study

Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other non-linear phenomena in complex human and natural systems. Increasing amounts of temporal network data are now becoming available to study such spreading processes of behaviours, opinions, ideas, diseases and innovations to test hypotheses regarding their specific properties. To this end, we here present a methodology based on dose–response functions and hypothesis testing using surrogate data models that randomise most aspects of the empirical data while conserving certain structures relevant to contagion, group or homophily dynamics. We demonstrate this methodology for synthetic temporal network data of spreading processes generated by the adaptive voter model. Furthermore, we apply it to empirical temporal network data from the Copenhagen Networks Study. This data set provides a physically-close-contact network between several hundreds of university students participating in the study over the course of 3 months. We study the potential spreading dynamics of the health-related behaviour “regularly going to the fitness studio” on this network. Based on a hierarchy of surrogate data models, we find that our method neither provides significant evidence for an influence of a dose–response-type network spreading process in this data set, nor significant evidence for homophily. The empirical dynamics in exercise behaviour are likely better described by individual features such as the disposition towards the behaviour, and the persistence to maintain it, as well as external influences affecting the whole group, and the non-trivial network structure. The proposed methodology is generic and promising also for applications to other temporal network data sets and traits of interest.

Building surrogate temporal network data from observed backbones.

Many systems of socioeconomic interests find a convenient representation in the form of temporal networks, i.e., sets of nodes and interactions occurring at specified times. In the corresponding data sets, however, crucial elements coexist with nonessential ones and noise. Several methods have thus been proposed to extract a "network backbone," i.e., the set of most important links in a network data set. The outcome of such methods can be seen as compressed versions of the original data. However, the question of how to practically use such reduced views of the data has not been tackled: for instance, using them directly in numerical simulations of processes on networks might lead to important biases. Overall, such reduced views of the data might not be actionable without an adequate decompression method. Here, we address this issue by putting forward and exploring several systematic procedures to build surrogate data from various kinds of temporal network backbones. In particular, we explore how much information about the original data needs to be retained alongside the backbone so that the surrogate data can be used in data-driven numerical simulations of spreading processes on a wide range of spreading parameters. We illustrate our results using empirical temporal networks with a broad variety of structures and properties. Our results give hints on how to best summarize complex data sets so that they remain actionable. Moreover, they show how ensembles of surrogate data with similar properties can be obtained from an original single data set, without any modeling assumptions.

Predicting partially observed processes on temporal networks by Dynamics-Aware Node Embeddings (DyANE)

Low-dimensional vector representations of network nodes have proven successful to feed graph data to machine learning algorithms and to improve performance across diverse tasks. Most of the embedding techniques, however, have been developed with the goal of achieving dense, low-dimensional encoding of network structure and patterns. Here, we present a node embedding technique aimed at providing low-dimensional feature vectors that are informative of dynamical processes occurring over temporal networks – rather than of the network structure itself – with the goal of enabling prediction tasks related to the evolution and outcome of these processes. We achieve this by using a lossless modified supra-adjacency representation of temporal networks and building on standard embedding techniques for static graphs based on random walks. We show that the resulting embedding vectors are useful for prediction tasks related to paradigmatic dynamical processes, namely epidemic spreading over empirical temporal networks. In particular, we illustrate the performance of our approach for the prediction of nodes’ epidemic states in single instances of a spreading process. We show how framing this task as a supervised multi-label classification task on the embedding vectors allows us to estimate the temporal evolution of the entire system from a partial sampling of nodes at random times, with potential impact for nowcasting infectious disease dynamics.

Detecting Dynamic States of Temporal Networks Using Connection Series Tensors

Many temporal networks exhibit multiple system states, such as weekday and weekend patterns in social contact networks. The detection of such distinct states in temporal network data has recently been studied as it helps reveal underlying dynamical processes. A commonly used method is network aggregation over a time window, which aggregates a subsequence of multiple network snapshots into one static network. This method, however, necessarily discards temporal dynamics within the time window. Here we propose a new method for detecting dynamic states in temporal networks using connection series (i.e., time series of connection status) between nodes. Our method consists of the construction of connection series tensors over nonoverlapping time windows, similarity measurement between these tensors, and community detection in the similarity network of those time windows. Experiments with empirical temporal network data demonstrated that our method outperformed the conventional approach using simple network aggregation in revealing interpretable system states. In addition, our method allows users to analyze hierarchical temporal structures and to uncover dynamic states at different spatial/temporal resolutions.

Universal evolution patterns of degree assortativity in social networks

Degree assortativity characterizes the propensity for large-degree nodes to connect to other large-degree nodes and low-degree to low-degree. It is important to describe the forces forming the network and to predict the behavior of dynamic systems on the network. To understand the evolutionary dynamics of degree assortativity, we collect a variety of empirical temporal social networks, and find that there is a universal pattern that the degree assortativity increases at the beginning of evolution and then decreases to a long-lasting stable level. We develop a bidirectional selection model to re-construct the evolution dynamic. In our model, we assume each individual has a social status that—in analogy to Pareto’s wealth distribution —follows a power-law distribution. We assume the social status determines the probability of an interaction between two actors. By varying the ratio of link establishment from within the same status level to across different status levels, the simulated network can be tuned to be assortative or disassortative. This suggests that the rise-and-fall pattern of degree assortativity is a consequence of the different network-forming forces active at different mixing of status. Our simulations indicate that Pareto social status distribution in the population may drive the social evolution in a way of self-optimization to promote the social interaction among individuals and the status gap plays an important role for the assortativity of the social network.

Empirical Mode Decomposition and Temporal Convolutional Networks for Remaining Useful Life Estimation

Remaining useful life (RUL) prediction plays an important role in guaranteeing safe operation and reducing maintenance cost in modern industry. In this paper, we present a novel deep learning method for RUL estimation based on time empirical mode decomposition (EMD) and temporal convolutional networks (TCN). The proposed framework can effectively reveal the non-stationary characteristics of bearing degradation signals and acquire time-series degradation signals which namely intrinsic mode functions through empirical mode decomposition. Furthermore, the feature information is used as the input to convolution layer and trained by TCN to predict remaining useful life. The proposed EMD–TCN model structure maintains a superior result compared to several state-of-the-art convolutional algorithms on public data sets. Experimental results show that the average score of EMD–TCN model is improved by 10–20% than traditional convolutional algorithms.

Impact of misinformation in temporal network epidemiology

AbstractWe investigate the impact of misinformation about the contact structure on the ability to predict disease outbreaks. We base our study on 31 empirical temporal networks and tune the frequencies in errors in the node identities or time stamps of contacts. We find that for both these spreading scenarios, the maximal misprediction of both the outbreak size and time to extinction follows an stretched exponential convergence as a function of the error frequency. We furthermore determine the temporal-network structural factors influencing the parameters of this convergence.

Navigating temporal networks

Navigation on graphs is the problem how an agent walking on the graph can get from a source to a target with limited information about the graph. The information and the way to exploit it can vary. In this paper, we study navigation on temporal networks—networks where we have explicit information about the time of the interaction, not only who interacts with whom. We contrast a type of greedy navigation – where agents follow paths that would have worked well in the past – with two strategies that do not exploit the additional information. We test these on empirical temporal network data sets. The greedy navigation finds the targets faster and more reliably than the reference strategies, meaning that there are correlations in the real temporal networks that can be exploited. We find that both topological and temporal structures affect the navigation.

Risk of Coinfection Outbreaks in Temporal Networks: A Case Study of a Hospital Contact Network

We study the spreading of cooperative infections in an empirical temporal network of contacts between people, including health care workers and patients, in a hospital. The system exhibits a phase transition leading to one or several endemic branches, depending on the connectivity pattern and the temporal correlations. There are two endemic branches in the original setting and the non-cooperative case. However, the cooperative interaction between infections reinforces the upper branch, leading to a smaller epidemic threshold and a higher probability for having a big outbreak. We show the microscopic mechanisms leading to these differences, characterize three different risks, and use the influenza features as an example for this dynamics.

Spectral Analysis of Epidemic Thresholds of Temporal Networks.

Many complex systems can be modeled as temporal networks with time-evolving connections. The influence of their characteristics on epidemic spreading is analyzed in a susceptible-infected-susceptible epidemic model illustrated by the discrete-time Markov chain approach. We develop the analytical epidemic thresholds in terms of the spectral radius of weighted adjacency matrix by averaging temporal networks, e.g., periodic, nonperiodic Markovian networks, and a special nonperiodic non-Markovian network (the link activation network) in time. We discuss the impacts of statistical characteristics, e.g., bursts and duration heterogeneity, as well as time-reversed characteristic on epidemic thresholds. We confirm the tightness of the proposed epidemic thresholds with numerical simulations on seven artificial and empirical temporal networks and show that the epidemic threshold of our theory is more precise than those of previous studies.

Structural Controllability of Temporal Networks with a Single Switching Controller.

Temporal network, whose topology evolves with time, is an important class of complex networks. Temporal trees of a temporal network describe the necessary edges sustaining the network as well as their active time points. By a switching controller which properly selects its location with time, temporal trees are used to improve the controllability of the network. Therefore, more nodes are controlled within the limited time. Several switching strategies to efficiently select the location of the controller are designed, which are verified with synthetic and empirical temporal networks to achieve better control performance.

EIGENVECTOR-BASED CENTRALITY MEASURES FOR TEMPORAL NETWORKS.

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NT × NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.

Detection and localization of change points in temporal networks with the aid of stochastic block models

A framework based on generalized hierarchical random graphs (GHRGs) for the detection of change points in the structure of temporal networks has recently been developed by Peel and Clauset (2015 Proc. 29th AAAI Conf. on Artificial Intelligence). We build on this methodology and extend it to also include the versatile stochastic block models (SBMs) as a parametric family for reconstructing the empirical networks. We use five different techniques for change point detection on prototypical temporal networks, including empirical and synthetic ones. We find that none of the considered methods can consistently outperform the others when it comes to detecting and locating the expected change points in empirical temporal networks. With respect to the precision and the recall of the results of the change points, we find that the method based on a degree-corrected SBM has better recall properties than other dedicated methods, especially for sparse networks and smaller sliding time window widths.

Higher-order aggregate networks in the analysis of temporal networks: path structures and centralities

Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in which links occur in real-world temporal networks affects causality structures and thus the evolution of dynamical processes, and ii) higher-order aggregate representations of temporal networks can be used to analytically study the effect of these order correlations on dynamical processes. In this article we analyze the effect of order correlations on path-based centrality measures in real-world temporal networks. Analyzing temporal equivalents of betweenness, closeness and reach centrality in six empirical temporal networks, we first show that an analysis of the commonly used static, time-aggregated representation can give misleading results about the actual importance of nodes. We further study higher-order time-aggregated networks, a recently proposed generalization of the commonly applied static, time-aggregated representation of temporal networks. Here, we particularly define path-based centrality measures based on second-order aggregate networks, empirically validating that node centralities calculated in this way better capture the true temporal centralities of nodes than node centralities calculated based on the commonly used static (first-order) representation. Apart from providing a simple and practical method for the approximation of path-based centralities in temporal networks, our results highlight interesting perspectives for the use of higher-order aggregate networks in the analysis of time-stamped network data.