Time-varying Graphs Research Articles

Tfgcn: a time-varying fuzzy graph convolutional network for multi-sensor traffic flow forecasting

Tfgcn: a time-varying fuzzy graph convolutional network for multi-sensor traffic flow forecasting

Privacy Preserving Distributed Bandit Residual Feedback Online Optimization Over Time-Varying Unbalanced Graphs

Privacy Preserving Distributed Bandit Residual Feedback Online Optimization Over Time-Varying Unbalanced Graphs

Locating a black hole in a dynamic ring

In networked environments supporting mobile agents, a pressing problem is the presence of network sites harmful for the agents. In this paper we consider the danger posed by a node that destroys any incoming agent without leaving any trace. Such a dangerous node is known in the literature as a black hole (Bh). The problem of a team of system agents determining its location, known as black hole search (Bhs ), has been extensively studied in the literature under a variety of assumptions, both in synchronous and asynchronous settings. The main complexity parameter of Bhsis the number of system agents (called size) needed to solve the problem; other parameters are the number of moves (called cost) performed by the agents, and the time until termination.In the existing literature, with only a couple of exceptions, all results are based on a common assumption that the network is static, i.e. its topology does not change in time. We consider instead the Bhswhen the network is dynamic: the link structure of the graph changes over time. While time-varying graphs have been the focus of intense research in the last two decades, very little is known on the problem of locating the Bh in such networks.In this paper, we contribute to fill this research gap by studying Bhsin dynamic ring networks, focusing on the 1-interval connectivity adversarial dynamics. Feasibility and complexity of the problem depend on many factors, specifically on the size n of the ring, whether or not n is known, and the type of inter-agent communication (whiteboards, tokens, face-to-face, visual). In this paper, we provide a complete feasibility characterization presenting size optimal algorithms. Furthermore, we establish lower bounds on the cost and time of size-optimal solutions and show that our algorithms achieve those bounds.

Tai Chi Practice Buffers Aging Effects in Functional Brain Connectivity.

Tai Chi (TC) practice has been shown to improve both cognitive and physical function in older adults. However, the neural mechanisms underlying the benefits of TC remain unclear. Our primary aims are to explore whether distinct age-related and TC-practice-related relationships can be identified with respect to either temporal or spatial (within/between-network connectivity) differences. This cross-sectional study examined recurrent neural network dynamics, employing an adaptive, data-driven thresholding approach to source-localized resting-state EEG data in order to identify meaningful connections across time-varying graphs, using both temporal and spatial features derived from a hidden Markov model (HMM). Mann-Whitney U tests assessed between-group differences in temporal and spatial features by age and TC practice using either healthy younger adult controls (YACs, n = 15), healthy older adult controls (OACs, n = 15), or Tai Chi older adult practitioners (TCOAs, n = 15). Our results showed that aging is associated with decreased within-network and between-network functional connectivity (FC) across most brain networks. Conversely, TC practice appears to mitigate these age-related declines, showing increased FC within and between networks in older adults who practice TC compared to non-practicing older adults. These findings suggest that TC practice may abate age-related declines in neural network efficiency and stability, highlighting its potential as a non-pharmacological intervention for promoting healthy brain aging. This study furthers the triple-network model, showing that a balancing and reorientation of attention might be engaged not only through higher-order and top-down mechanisms (i.e., FPN/DAN) but also via the coupling of bottom-up, sensory-motor (i.e., SMN/VIN) networks.

Distributed Ishikawa algorithms for seeking the fixed points of multi-agent global operators over time-varying communication graphs

In this article, the problem of seeking fixed points for global operators over the time-varying graphs in a real Hilbert space is studied. The global operator is a linear combination of local operators, each local operator being accessed privately by one agent for less resource consumption. All agents form a network and they need to cooperate to solve problems. To this end, on the basis of the centralized Ishikawa iteration, the distributed Ishikawa algorithm (D-I) is first proposed. In the sequel, to predigest the calculational complexity, further considering the situation that only the random part of each operator coordinate is calculated in each iteration, the distributed block coordinate Ishikawa algorithm (D-BI) is also designed. The results indicate that the proposed D-I and D-BI algorithms can weakly converge to a fixed point of the multi-agent global operator. Eventually, we give a few numerical examples to illustrate practical benefits of the proposed algorithms.

Gegenbauer Graph Neural Networks for Time-Varying Signal Reconstruction.

Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series forecasting. Accurately capturing the spatio-temporal information inherent in these signals is crucial for effectively addressing these tasks. However, existing approaches relying on smoothness assumptions of temporal differences and simple convex optimization techniques that have inherent limitations. To address these challenges, we propose a novel approach that incorporates a learning module to enhance the accuracy of the downstream task. To this end, we introduce the Gegenbauer-based graph convolutional (GegenConv) operator, which is a generalization of the conventional Chebyshev graph convolution by leveraging the theory of Gegenbauer polynomials. By deviating from traditional convex problems, we expand the complexity of the model and offer a more accurate solution for recovering time-varying graph signals. Building upon GegenConv, we design the Gegenbauer-based time graph neural network (GegenGNN) architecture, which adopts an encoder-decoder structure. Likewise, our approach also uses a dedicated loss function that incorporates a mean squared error (MSE) component alongside Sobolev smoothness regularization. This combination enables GegenGNN to capture both the fidelity to ground truth and the underlying smoothness properties of the signals, enhancing the reconstruction performance. We conduct extensive experiments on real datasets to evaluate the effectiveness of our proposed approach. The experimental results demonstrate that GegenGNN outperforms state-of-the-art methods, showcasing its superior capability in recovering time-varying graph signals.

Directed brain interactions over time: A resting-state EEG comparison between schizophrenia and healthy individuals

Understanding the neurophysiological mechanisms of schizophrenia (SZ) is one of the challenges of neuroscience. Many anatomical and functional studies have pointed to problems in brain connectivity in SZ individuals. However, little is known about the relationships between specific brain regions and impairments in brain connectivity in SZ individuals. Herein we propose a new approach using time-varying graphs and the motif synchronization method to build dynamic brain functional networks (BFNs). Dynamic BFNs were constructed from resting-state electroencephalography (rs-EEG) of 14 schizophrenia (SZ) individuals and 14 healthy controls (HCs). BFNs were evaluated based on the percentage of synchronization importance between a pair of regions (considering external and internal interactions) over time. We found differences in the directed interaction between brain regions in SZ individuals compared to the control group. Our method revealed low bilaterally directed interactions between the temporal lobes in SZ individuals compared to HCs, indicating a potential link between altered brain connectivity and the characteristic symptoms of schizophrenia. From a clinical perspective, these results shed light on developing new therapeutic approaches targeting these specific neural interactions that are altered in individuals with SZ. This knowledge allows the application of better interventions focused on restoring or compensating for interrupted connectivity patterns.

Joint time-vertex linear canonical transform

The emergence of graph signal processing (GSP) has spurred a deep interest in signals that naturally reside on irregularly structured data kernels, such as those found in social, transportation, and sensor networks. Recently, concepts and applications related to time-varying graph signal analysis have matured, linking temporal signal processing techniques with innovative tools in GSP. In this paper, similar to the extension of the graph fractional Fourier transform to the graph linear canonical transform, we define the joint time-vertex linear canonical transform (JLCT) and its properties. This transformation extends the joint time-vertex Fourier transform (JFT) and fractional Fourier transform (JFRFT), broadening the Fourier analysis in both time and vertex domains into the domain of the linear canonical transform (LCT). This offers an enhanced set of the LCT analysis tools for joint time-vertex processing. Applications of the JLCT in dynamic mesh denoising, clustering, and energy compactness demonstrate that JLCT can enhance regression and learning tasks, and can refine and improve the performance of the JFT and the JFRFT.

Temporal-Difference Graph-Based Optimization for High-Quality Reconstruction of MODIS NDVI Data

The Normalized Difference Vegetation Index (NDVI) is a crucial remote-sensing metric for assessing land surface vegetation greenness, essential for various studies encompassing phenology, ecology, hydrology, etc. However, effective applications of NDVI data are hindered by data noise due to factors such as cloud contamination, posing challenges for accurate observation. In this study, we proposed a novel approach for employing a Temporal-Difference Graph (TDG) method to reconstruct low-quality pixels in NDVI data. Regarding spatio-temporal NDVI data as a time-varying graph signal, the developed method utilized an optimization algorithm to maximize the spatial smoothness of temporal differences while preserving the spatial NDVI pattern. This approach was further evaluated by reconstructing MODIS/Terra Vegetation Indices 16-Day L3 Global 250 m Grid (MOD13Q1) products over Northwest China. Through quantitative comparison with a previous state-of-the-art method, the Savitzky–Golay (SG) filter method, the obtained results demonstrated the superior performance of the TDG method, and highly accurate results were achieved in both the temporal and spatial domains irrespective of noise types (positively-biased, negatively-biased, or linearly-interpolated noise). In addition, the TDG-based optimization approach shows great robustness to noise intensity within spatio-temporal NDVI data, suggesting promising prospects for its application to similar datasets.

HOGN-TVGN: Human-inspired Embodied Object Goal Navigation based on Time-varying Knowledge Graph Inference Networks for Robots

Object goal navigation tasks are critical for robots operating in unfamiliar environments, where they must locate specific objects using visual cues. The ability to leverage prior knowledge significantly enhances a robot’s associative capabilities, leading to improved navigation performance. However, existing methods struggle with the generalization challenge when transferring navigation models to new environments, a key issue addressed in this paper. To overcome this challenge, on the one hand, a time-varying knowledge graph is proposed to update the prior knowledge graph with context vectors derived from co-occurrence objects in the current observation. This approach prioritizes local graphs centered around the target and co-occurring objects, allowing for efficient and accurate target localization. Furthermore, the dynamic updating mechanism facilitates efficient exploration in new scenarios. On the other hand, to embed prior knowledge more rationally in the reinforcement learning-based navigation strategy, a time-varying knowledge graph inference network (TVGN) is presented. The TVGN utilizes context vectors and global spatial semantic information to perceive and understand the environment in real-time. It formulates navigation strategies based on the precise goal information encoded within the graph, thereby enhancing the robot’s efficiency in reaching the target. Based on the widely applied dataset AI2-THOR, extensive comparative experiments are conducted to illustrate the effectiveness of the proposed method. Experimental results indicate that our model outperforms state-of-the-art competitors, demonstrating notable advantages in navigation effectiveness and efficiency in previously unseen environments.

TVGCN: Time-varying graph convolutional networks for multivariate and multifeature spatiotemporal series prediction.

Spatiotemporal (ST) graph modeling has garnered increasing attention recently. Most existing methods rely on a predefined graph structure or construct a single learnable graph throughout training. However, it is challenging to use a predefined graph structure to capture dynamic ST changes effectively due to evolving node relationships over time. Furthermore, these methods typically utilize only the original data, neglecting external temporal factors. Therefore, we put forward a novel time-varying graph convolutional network model that integrates external factors for multifeature ST series prediction. Firstly, we construct a time-varying adjacency matrix using attention to capture dynamic spatial relationships among nodes. The graph structure adapts over time during training, validation, and testing phases. Then, we model temporal dependence by dilated causal convolution, leveraging gated activation unit and residual connection. Notably, the prediction accuracy is enhanced through the incorporation of embedding absolute time and the fusion of multifeature. This model has been applied to three real-world multifeature datasets, achieving state-of-the-art performance in all cases. Experiments show that the method has high accuracy and robustness when applied to multifeature and multivariate ST series problems.

Distributed online constrained convex optimization with event-triggered communication

This paper focuses on the distributed online convex optimization problem with time-varying inequality constraints over a network of agents, where each agent collaborates with its neighboring agents to minimize the cumulative network-wide loss over time. To reduce communication overhead between the agents, we propose a distributed event-triggered online primal–dual algorithm over a time-varying directed graph. With several classes of appropriately chose decreasing parameter sequences and non-increasing event-triggered threshold sequences, we establish dynamic network regret and network cumulative constraint violation bounds. Finally, a numerical simulation example is provided to verify the theoretical results.

Multilayer time-variant network edges synchronization method

In this work, we propose a method for measuring synchronization between the edges of a pair of networks with connections that vary over time. The product of this method is an Incidence-Fidelity network, indicating the intensity of edge synchronization during a time interval. Two distinct validations were performed: in the first, we employed time-varying multilayer graphs with random connections to validate the algorithm; and in the second, we used the coupled Rössler oscillator to validate the method. In the algorithm validation, we compared the algebraically predicted results with the results obtained by using random networks. In the method validation, we used the coupled Rössler oscillator to generate time series representing the existence of two edges, one in each layer of the time-varying multilayer graphs. We assessed the relationship between the pre-defined coupling values and the achieved synchronization indices. In the application of our method, we considered time series of 17 years of climate data for the Normalized Difference Vegetation Index (NDVI) and precipitation for all municipalities in the state of Bahia, Brazil. To do so, we first obtained the individual layers of the multilayer network using a motif synchronization method. From the individual layers, we generated the Interlayer Incidence-Fidelity network. The obtained Interlayer Incidence-Fidelity network for the NDVI and precipitation pair reflects a connection pattern that incorporates the configurations of the individual layers. This is because synchronizations are primarily distributed in the more interconnected regions of the individual layers. The Interlayer Incidence-Fidelity networks generated by our method can identify synchronization patterns in the evolution of relationships between networks over time. This method presents a promising tool for evaluating synchronization between networks, generating a weighted network that quantifies the different levels of temporal synchronization for each edge in the networks.

Multiscale dynamic graph signal analysis

We consider the problem of decomposing a time-varying graph signal into its constituent amplitude- and frequency-modulated components and inferring their dynamic functional connectivity structures in a data-driven manner, referred to as graph mode decomposition (GMD). The currently available method for GMD obtains static connectivity structures, limiting its applicability to real-life data. Further, the performance of the method relies critically on the accurate prior knowledge of the number of components to be extracted. We address those key limitations by presenting two approaches: (1) a two-stage method for obtaining the graph modes as well as corresponding connectivity structures by solving two separate optimization problems, and (2) a joint optimization formulation to achieve that task. The proposed optimization formulations include a prior to account for the time variation of graph edge weights. Moreover, we use a successive scheme to solve the problems which alleviates the limitation of having to specify the number of decomposed components a priori — improving the accuracy and data-driven capability while reducing the computational requirement of the methods. The performance of these methods is validated on a wide range of synthetic and real data sets. We also provide a public toolbox containing the MATLAB codes of the proposed methods.

LocalTGEP: A Lightweight Edge Partitioner for Time-Varying Graph

Graph edge partitioning (GEP), the allocation of edges into different parts through cut vertices, is essential for the analytics of large-scale graphs. Most GEP models cannot be directly applied to a time-varying graph unless repartitioning the entire graph, which leads to a large consumption of resources. Although a few studies have focused on time-varying graph edge partitioning, they have ignored the memory consumption during the partitioning process. Therefore, a lightweight edge partitioner, referred to as LocalTGEP, broadening the application to time-varying graphs, is proposed herein. Three superiorities of LocalTGEP are highlighted as follows: 1) A satisfactory partitioning quality for a time-varying graph can be achieved without requiring global information owing to the local edge partitioning. 2) Memory consumption of the partitioner is significantly reduced using a novel storage framework of graph data in LocalTGEP. 3) The quality and efficiency of time-varying graph edge partitioning are optimized by designing the push and pop stages in LocalTGEP. Extensive experimental results obtained on 12 real-world graphs demonstrate that LocalTGEP outperforms rival algorithms in terms of memory consumption, partitioning quality, and efficiency.

Advancing Marine-Bearing Capacity and Economic Growth: A Comprehensive Analysis of Blue Economy Resilience, Network Evolution, and Technological Influences in China’s Coastal Areas

This study presents a groundbreaking approach to evaluating the resilience of China’s blue economy, shedding light on its critical role in promoting sustainable development along the nation’s coastlines. By employing advanced methodologies such as social network analysis and the time-varying effect random graph model (TERGM), our research meticulously examines the period from 2007 to 2019. It uncovers the complex dynamics of resilience, focusing on the adversities of unbalanced growth and pinpointing pivotal factors which shape this resilience, including the stability of the marine economy, the rigor of environmental regulations, and the impact of technological progress. Through a strategic compilation of indicators, our analysis offers a detailed perspective on the multi-faceted nature of blue economy resilience. The outcomes underscore the necessity of enhancing network effectiveness and implementing specific measures to encourage sustainable expansion in coastal domains. Leveraging these insights, we advocate for targeted strategies to refine the resilience network’s framework, aiming to bolster the sustainable evolution of marine economic activities. This study not only deepens the understanding of marine economic resilience but also charts a course for achieving a resilient and sustainable blue economy. It stands as an indispensable guide for policymakers and scholars in the realm of marine economics, offering a blueprint for navigating the challenges and opportunities within this vital sector.

A cop and robber game on edge-periodic temporal graphs

We introduce a cops and robbers game with one cop and one robber on a special type of time-varying graphs (TVGs), namely edge-periodic graphs. These are TVGs in which, for each edge e, a binary string τ(e) is given such that the edge e is present in time step t if and only if τ(e) contains a 1 at position tmod|τ(e)|. This periodicity allows for a compact representation of infinite TVGs. We prove that even for very simple underlying graphs, i.e., directed and undirected cycles, the problem of deciding whether a cop-winning strategy exists is NP-hard and W[1]-hard parameterized by the number of vertices. Furthermore, we show that this decision problem can be solved on general edge-periodic graphs in PSPACE. Finally, we present tight bounds on the minimum length of a directed or undirected cycle that guarantees the cycle to be robber-winning.

An Expository Examination of Temporally Evolving Graph-Based Approaches for the Visual Investigation of Autonomous Driving

With the continuous advancement of autonomous driving technology, visual analysis techniques have emerged as a prominent research topic. The data generated by autonomous driving is large-scale and time-varying, yet more than existing visual analytics methods are required to deal with such complex data effectively. Time-varying diagrams can be used to model and visualize the dynamic relationships in various complex systems and can visually describe the data trends in autonomous driving systems. To this end, this paper introduces a time-varying graph-based method for visual analysis in autonomous driving. The proposed method employs a graph structure to represent the relative positional relationships between the target and obstacle interferences. By incorporating the time dimension, a time-varying graph model is constructed. The method explores the characteristic changes of nodes in the graph at different time instances, establishing feature expressions that differentiate target and obstacle motion patterns. The analysis demonstrates that the feature vector centrality in the time-varying graph effectively captures the distinctions in motion patterns between targets and obstacles. These features can be utilized for accurate target and obstacle recognition, achieving high recognition accuracy. To evaluate the proposed time-varying graph-based visual analytic autopilot method, a comparative study is conducted against traditional visual analytic methods such as the frame differencing method and advanced visual analytic methods like visual lidar odometry and mapping. Robustness, accuracy, and resource consumption experiments are performed using the publicly available KITTI dataset to analyze and compare the three methods. The experimental results show that the proposed time-varying graph-based method exhibits superior accuracy and robustness. This study offers valuable insights and solution ideas for developing deep integration between intelligent networked vehicles and intelligent transportation. It provides a reference for advancing intelligent transportation systems and their integration with autonomous driving technologies.

Time-varying graph learning from smooth and stationary graph signals with hidden nodes

Learning graph structure from observed signals over graph is a crucial task in many graph signal processing (GSP) applications. Existing approaches focus on inferring static graph, typically assuming that all nodes are available. However, these approaches ignore the situation where only a subset of nodes are available from spatiotemporal measurements, and the remaining nodes are never observed due to application-specific constraints, resulting in time-varying graph estimation accuracy declines dramatically. To handle this problem, we propose a framework that consider the presence of hidden nodes to identify time-varying graph. Specifically, we assume that the graph signals are smooth and stationary on the graphs and only a small number of edges are allowed to change between two consecutive graphs. With these assumptions, we present a challenging time-varying graph inference problem, which models the influence of hidden nodes in terms of estimating the graph-shift operator matrices that have a form of graph Laplacian. Moreover, we emphasize similar edge pattern (column-sparsity) between different graphs. Finally, our method is evaluated on both synthetic and real-world data. The experimental results demonstrate the advantage of our method when compared to existing benchmarking methods.

Multi-competitive time-varying networked SIS model with an infrastructure network

The paper studies the problem of the spread of multi-competitive viruses across a (time-varying) population network and an infrastructure network. To this end, we devise a variant of the classic (networked) susceptible–infected-susceptible (SIS) model called the multi-competitive time-varying networked susceptible-infected-water-susceptible (SIWS) model. We establish a sufficient condition for exponentially fast eradication of a virus when a) the graph structure does not change over time; b) the graph structure possibly changes with time, interactions between individuals are symmetric, and all individuals have the same healing and infection rate; and c) the graph is directed and is slowly-varying, and not all individuals necessarily have the same healing and infection rates. We also show that the aforementioned conditions for eradication of a virus are robust to variations in the graph structure of the population network provided the variations are not too large. For the case of time-invariant graphs, we give a lower bound on the number of equilibria that our system possesses. Finally, we provide an in-depth set of simulations that not only illustrate the theoretical findings of this paper but also provide insights into the endemic behavior for the case of time-varying graphs.