Network Reconstruction Problem Research Articles

LSTM network optimization and task network construction based on heuristic algorithm

This work aims to advance the security management of complex networks to better align with evolving societal needs. The work employs the Ant Colony Optimization algorithm in conjunction with Long Short-Term Memory neural networks to reconstruct and optimize task networks derived from time series data. Additionally, a trend-based noise smoothing scheme is introduced to mitigate data noise effectively. The approach entails a thorough analysis of historical data, followed by applying trend-based noise smoothing, rendering the processed data more scientifically robust. Subsequently, the network reconstruction problem for time series data originating from one-dimensional dynamic equations is addressed using an algorithm based on the principles of Stochastic Gradient Descent (SGD). This algorithm decomposes time series data into smaller samples and yields optimal learning outcomes in conjunction with an adaptive learning rate SGD approach. Experimental results corroborate the remarkable fidelity of the weight matrix reconstructed by this algorithm to the true weight matrix. Moreover, the algorithm exhibits efficient convergence with increasing data volume, manifesting shorter time requirements per iteration while ensuring the attainment of optimal solutions. When the sample size remains constant, the algorithm’s execution time is directly proportional to the square of the number of nodes. Conversely, as the sample size scales, the SGD algorithm capitalizes on the availability of more information, resulting in improved learning outcomes. Notably, when the noise standard deviation is 0.01, models predicated on SGD and the Least-Squares Method (LSM) demonstrate reduced errors compared to instances with a noise standard deviation of 0.1, highlighting the sensitivity of LSM to noise. The proposed methodology offers valuable insights for advancing research in complex network studies.

Optimal Unmanned Combat System-of-Systems Reconstruction Strategy with Heterogeneous Cost via Deep Reinforcement Learning

The unmanned combat system-of-systems (UCSoS) in modern warfare is comprised of various interconnected entities that work together to support mission accomplishment. The soaring number of entities makes the UCSoS fragile and susceptible to triggering cascading effects when exposed to uncertain disturbances such as attacks or failures. Reconfiguring the UCSoS to restore its effectiveness in a self-coordinated and adaptive manner based on the battlefield situation and operational requirements has attracted increasing attention. In this paper, we focus on the UCSoS reconstruction with heterogeneous costs, where the collaboration nodes may have different reconstruction costs. Specifically, we adopt the heterogeneous network to capture the interdependencies among combat entities and propose a more representative metric to evaluate the UCSoS reconstruction effectiveness. Next, we model the combat network reconstruction problem with heterogeneous costs as a nonlinear optimization problem and prove its NP-hardness. Then, we propose an approach called SoS-Restorer, which is based on deep reinforcement learning (DRL), to address the UCSoS reconstruction problem. The results show that SoS-Restorer can quickly generate reconstruction strategies and improve the operational capabilities of the UCSoS by about 20∼60% compared to the baseline algorithm. Furthermore, even when the size of the UCSoS exceeds that of the training data, SoS-Restorer exhibits robust generalization capability and can efficiently produce satisfactory results in real time.

X-distribution: Retraceable Power-law Exponent of Complex Networks

Network modeling has been explored extensively by means of theoretical analysis as well as numerical simulations for Network Reconstruction (NR). The network reconstruction problem requires the estimation of the power-law exponent (γ) of a given input network. Thus, the effectiveness of the NR solution depends on the accuracy of the calculation of γ. In this article, we re-examine the degree distribution-based estimation of γ, which is not very accurate due to approximations. We propose X -distribution, which is more accurate than degree distribution. Various state-of-the-art network models, including CPM, NRM, RefOrCite2, BA, CDPAM, and DMS, are considered for simulation purposes, and simulated results support the proposed claim. Further, we apply X -distribution over several real-world networks to calculate their power-law exponents, which differ from those calculated using respective degree distributions. It is observed that X -distributions exhibit more linearity (straight line) on the log-log scale than degree distributions. Thus, X -distribution is more suitable for the evaluation of power-law exponent using linear fitting (on the log-log scale). The MATLAB implementation of power-law exponent (γ) calculation using X -distribution for different network models and the real-world datasets used in our experiments are available at https://github.com/Aikta-Arya/X-distribution-Retraceable-Power-Law-Exponent-of-Complex-Networks.git .

Reconstructing networks via discrete state dynamical data: A mini-review

The inference of network structure from dynamic data is one of the most challenging scientific problems in network science. To address this issue, researchers have proposed various approaches regarding different types of dynamical data. Since many real evolution processes or social phenomena can be described by discrete state dynamical systems, such as the spreading of epidemic, the evolution of opinions, and the cooperation behaviors, network reconstruction methods driven by discrete state dynamical data were also widely studied. In this letter, we provide a mini-review of recent progresses for reconstructing networks based on discrete state dynamical data. These studies encompass network reconstruction problems where the dynamical processes are known, as well as those where the dynamics are unknown, and extend to the reconstruction of higher-order networks. Finally, we discuss the remaining challenges in this field.

General optimization framework for accurate and efficient reconstruction of symmetric complex networks from dynamical data.

The challenging problem of network reconstruction from dynamical data can in general be formulated as an optimization task of solving multiple linear equations. Existing approaches are of the two types: Point-by-point (PBP) and global methods. The local PBP method is computationally efficient, but the accuracies of its solutions are somehow low, while a global method has the opposite traits: High accuracy and high computational cost. Taking advantage of the network symmetry, we develop a novel framework integrating the advantages of both the PBP and global methods while avoiding their shortcomings: i.e., high reconstruction accuracy is guaranteed, but the computational cost is orders of magnitude lower than that of the global methods in the literature. The mathematical principle underlying our framework is block coordinate descent (BCD) for solving optimization problems, where the various blocks are determined by the network symmetry. The reconstruction framework is validated by numerical examples with a variety of network structures (i.e., sparse and dense networks) and dynamical processes. Our success is a demonstration that the general principle of exploiting symmetry can be extended to tackling the challenging inverse problem or reverse engineering of complex networks. Since solving a large number of linear equationsis key to a plethora of problems in science and engineering, our BCD-based network reconstruction framework will find broader applications.

A Multiobjective Evolutionary Approach for Solving Large-Scale Network Reconstruction Problems via Logistic Principal Component Analysis.

Currently, the problem of uncovering complex network structure and dynamics from time series is prominent in many fields. Despite the recent progress in this area, reconstructing large-scale networks from limited data remains a tough problem. Existing works treat connections of nodes as continuous values, leaving a challenge of setting a proper cut-off value to distinguish whether the connections exist or not. Besides, their performances on large-scale networks are far from satisfactory. Considering the reconstruction error and sparsity as two objectives, this article proposes a subspace learning-based evolutionary multiobjective network reconstruction algorithm, called SLEMO-NR, to solve the aforementioned problems. In the evolutionary process, we assume that binary-coded individuals obey the Bernoulli distribution and can use the probability and natural parameter as alternative representations. Moreover, our approach utilizes the logistic principal component analysis (LPCA) to learn a subspace containing the features of the network structure. The offspring solutions are generated in the learned subspace and then can be mapped back to the original space via LPCA. Benefitting from the alternative representations, a preference-based local search operator (PLSO) is proposed to concentrate on finding solutions approximate to the true sparsity. The experimental results on synthetic networks and six real-world networks demonstrate that, due to the well-learned network structure subspace and the preference-based strategy, our approach is effective in reconstructing large-scale networks compared to six existing methods.

Distribution network reconfiguration control and protection method based on multi-source data interaction

Distribution network reconfiguration technology is the key technology of distribution network fault treatment and power supply recovery. Given the problem that the traditional distribution network reconfiguration algorithm needs a lot of power flow calculation and low efficiency to find the optimal target, the simulated annealing algorithm is proposed to optimize the computing speed and searching ability of the distribution network reconfiguration algorithm. Firstly, the information interaction technology of distribution network protection and control equipment is studied, and the real-time data rapid peer-to-peer exchange and data and information interaction model is built, which improves the fault detection and timely removal ability of the distribution network. Secondly, the simulated annealing algorithm is used to reduce the number of power flow calculations, reduce the calculation time, improve the calculation speed of network reconstruction problems, and ensure that the optimal or better network topology can be obtained. Finally, the simulation analysis of the IEEE37 node system verifies the effectiveness of the proposed reconfiguration protection method in a complex environment with massive access to distributed energy.

Evolutionary Multitasking Multilayer Network Reconstruction

Due to the multilayer nature of real-world systems, the problem of inferring multilayer network structures from nonlinear and complex dynamical systems is prominent in many fields, including engineering, biological, physical, and computer sciences. Many network reconstruction methods have been proposed to address this problem, but none of them consider the similarities among network reconstruction tasks at different component layers, which are inspired by topology correlations and dynamic couplings among different component layers. This article develops an evolutionary multitasking multilayer network reconstruction framework to make use of the correlations among different component layers to improve the reconstruction performance; we refer to this framework as EM2MNR. In EM2MNR, the multilayer network reconstruction problem is first established as a multitasking multilayer network reconstruction problem, where the goal of each task is to reconstruct the network structure of a component layer. In addition, multitasking multilayer network reconstruction problems are high dimensional, but existing evolutionary multitasking algorithms may have poor performance when dealing with optimization problems with a high-dimensional search space. Inspired by the sparsity of multilayer networks, EM2MNR employs the restricted Boltzmann machine to extract low effective features from the original decision space and then decides whether to conduct knowledge transfer on these features. To verify the performance of EM2MNR, this article also designs a test suite for multilayer network reconstruction problems. The experimental results demonstrate the significant improvement obtained by the proposed EM2MNR framework on 96 multilayer network reconstruction problems.

Network reconstruction problem for an epidemic reaction--diffusion system

Abstract We study the network reconstruction problem for an epidemic reaction–diffusion system. These systems are an extension of deterministic, compartmental models to a graph setting, where the reactions within the nodes are coupled by a diffusion dynamics. We study the influence of the diffusion rate and the network topology, on the reconstruction and prediction problems, both from a theoretical and experimental standpoint. Results first show that for almost every network, the reconstruction problem is well posed. Then, we show that the faster the diffusion dynamics, the harder the reconstruction, but that increasing the sampling rate may help in this respect. Second, we demonstrate that it is possible to classify symmetrical networks generating the same trajectories, and that the prediction problem can still be solved satisfyingly, even when the network topology makes exact reconstruction difficult.

Multilayer nonlinear dynamical network reconstruction from streaming data

Many complex, real-world dynamic systems need to be described using multilayer networks. Reconstruction of the multilayer nonlinear dynamic network structure from the observed streaming data is one of the core issues of dynamic system research. Although many methods have been proposed to reconstruct multilayer nonlinear dynamic networks from static data, they cannot reconstruct the multilayer network from streaming data. Because of the complexity of the problem, there is no nonlinear dynamic network reconstruction model and its optimization algorithm suitable for streaming data. To resolve this limitation, in this paper, a streaming data-driven multilayer dynamic network reconstruction framework called online multilayer network reconstruction (OMNR) is proposed. OMNR first establishes an online multilayer nonlinear dynamics network reconstruction model for streaming data and then proposes an online learning method based on follow-the-regularized-leader to optimize the reconstruction model. It considers only one case at a time to update the network structure; this is suitable for processing streaming data. Moreover, the space complexity of OMNR is very low and suitable for big-data tasks. Finally, using the Lorenz and Rossler dynamic systems of the multilayer network, it is verified that OMNR can solve the problem of multilayer dynamic network reconstruction driven by streaming data and fill the gap in the technology of multilayer nonlinear dynamic network reconstruction driven by streaming data.

A zero inflated log-normal model for inference of sparse microbial association networks.

The advent of high-throughput metagenomic sequencing has prompted the development of efficient taxonomic profiling methods allowing to measure the presence, abundance and phylogeny of organisms in a wide range of environmental samples. Multivariate sequence-derived abundance data further has the potential to enable inference of ecological associations between microbial populations, but several technical issues need to be accounted for, like the compositional nature of the data, its extreme sparsity and overdispersion, as well as the frequent need to operate in under-determined regimes. The ecological network reconstruction problem is frequently cast into the paradigm of Gaussian Graphical Models (GGMs) for which efficient structure inference algorithms are available, like the graphical lasso and neighborhood selection. Unfortunately, GGMs or variants thereof can not properly account for the extremely sparse patterns occurring in real-world metagenomic taxonomic profiles. In particular, structural zeros (as opposed to sampling zeros) corresponding to true absences of biological signals fail to be properly handled by most statistical methods. We present here a zero-inflated log-normal graphical model (available at https://github.com/vincentprost/Zi-LN) specifically aimed at handling such "biological" zeros, and demonstrate significant performance gains over state-of-the-art statistical methods for the inference of microbial association networks, with most notable gains obtained when analyzing taxonomic profiles displaying sparsity levels on par with real-world metagenomic datasets.

Exploratory Network Reconstruction with Sparse Archaeological Data and XTENT

This contribution discusses methods for reconstructing the links of past physical networks, based on archaeological site locations and mathematical models of few parameters. Networks are ubiquitous features of human culture. They structure the geographical patterning of the archaeological record strongly. But while material evidence of networked social interaction is abundant (e.g. similarities in artefact types and technologies), preserved physical remains of the networks (such as roads) are much rarer, making it difficult, if not impossible, to understand the spatial structure of cultural exchange and diffusion. This raises the intractably complex problem of optimal physical network reconstruction, based solely on the known locations of archaeological finds or sites. We address the tractable subproblem of plausible reconstruction of network links. Using a small sample set of Late Bronze Age settlement sites in and around the Mediterranean, we explore model-based network reconstruction from sparse and legacy archaeological data. A hierarchical model is provided by a network-adapted version of Renfrew and Level’s (1979) classic XTENT formula. We show that a GIS-based implementation, that utilises cost surfaces, offers significantly increased realism and analytical advantages. Our approach represents an alternative (with its specific strengths and weaknesses) to more data-intense and computationally complex approaches, such as agent-based models and simulations. The network reconstruction software used in this study (v.net.models) is available under an open source license.

Evolutionary multitasking network reconstruction from time series with online parameter estimation

Reconstructing the structure of complex networks from time series is beneficial to understanding and controlling the collective dynamics of networked systems. Existing network reconstruction algorithms can only deal with one network reconstruction problem at one time. However, real-world applications typically have multiple network reconstruction tasks and these tasks often relate to each other to certain extent. For the purpose of exploring similar network structure patterns in different tasks, we establish an evolutionary multitasking framework to simultaneously optimize double network reconstruction tasks. In the proposed method, each task is modeled as a single objective problem containing the reconstruction error and the l0-norm of the weight matrix, which takes both the reconstruction error and the structure error into consideration and deals with the NP-hard problem directly. Online parameter learning scheme is employed to learn the parameter automatically controlling the amount of genetic material to exchange, thus avoiding the negative transfer while allowing the useful information pass between tasks. In addition, the least absolute shrinkage and selection operator (LASSO) initialization is employed to further enhance the performance. We apply the evolutionary multitasking framework to reconstruct both synthetic and real networks of evolutionary game, resistor networks, and communication network dynamic models. The experimental results demonstrate that the proposal exhibits competitive performance against state-of-the-arts in terms of all evaluation measures.

Online Reconstruction of Complex Networks From Streaming Data.

The problem of reconstructing nonlinear and complex dynamical systems from available data or time series is prominent in many fields, including engineering, physical, computer, biological, and social sciences. Many methods have been proposed to address this problem and their performance is satisfactory. However, none of them can reconstruct network structure from large-scale real-time streaming data, which leads to the failure of real-time and online analysis or control of complex systems. In this article, to overcome the limitations of current methods, we first extend the network reconstruction problem (NRP) to online settings, and then develop a follow-the-regularized-leader (FTRL)-Proximal style method to address the online complex NRP; we refer to it as Online-NR. The performance of Online-NR is validated on synthetic evolutionary game network reconstruction datasets and eight real-world networks. The experimental results demonstrate that Online-NR can effectively solve the problem of online network reconstruction with large-scale real-time streaming data. Moreover, Online-NR outperforms or matches nine state-of-the-art network reconstruction methods.

A distribution network reconstruction method with DG and EV based on improved gravitation algorithm

In order to solve the problem of distribution network reconstruction with distributed generation (DG) and electric vehicle (EV), a multi-objective distribution network reconstruction model with DG and EV is established in this study. Two rules for opening the loop are proposed to reduce the probability of infeasible solutions. Some measures are proposed to improve traditional gravitational algorithm (GSA). Firstly, the particle swarm algorithm (PSO) is combined to improves the update formula of speed and position. In this way, the global search capability of the GSA is enhanced, which gives the best performance with respect to jump out of the local traps. Furthermore, the processing method for agents that cross the boundary is improved, which increases the diversity of samples while generating elite particles. Hence, this method can improve the efficiency of the algorithm. Finally, the variability of load, DG and EV is considered for dynamic reconstruction. The validity of the optimization algorithm and refactoring strategy are demonstrated by case studies in the paper.

An Evolutionary Multiobjective Framework for Complex Network Reconstruction Using Community Structure

The problem of inferring nonlinear and complex dynamical systems from available data is prominent in many fields, including engineering, biological, social, physical, and computer sciences. Many evolutionary algorithm (EA)-based network reconstruction methods have been proposed to address this problem, but they ignore several useful information of network structure, such as community structure, which widely exists in various complex networks. Inspired by the community structure, this article develops a community-based evolutionary multiobjective network reconstruction framework to promote the reconstruction performance of EA-based network reconstruction methods due to their good performance; we refer this framework as CEMO-NR. CEMO-NR is a generic framework and any population-based multiobjective metaheuristic algorithm can be employed as the base optimizer. CEMO-NR employs the community structure of networks to divide the original decision space into multiple small decision spaces, and then any multiobjective EA (MOEA) can be used to search for improved solutions in the reduced decision space. To verify the performance of CEMO-NR, this article also designs a test suite for complex network reconstruction problems. Three representative MOEAs are embedded into CEMO-NR and compared with their original versions, respectively. The experimental results have demonstrated the significant improvement benefiting from the proposed CEMO-NR in 30 multiobjective network reconstruction problems (MONRPs).

A Statistical Mechanics Approach to Systemic Risk under Bilateral Netting Agreements

We propose a statistical mechanics approach to the problem of financial network reconstruction and systemic risk when participants benefit from bilateral netting agreements. We apply physical reasoning to directly estimate individual financial liabilities from data on both total gross and net positions of total liabilities and total assets. We map this constrained network reconstruction problem to an energy-minimization one, to which we apply a Markov Chain Monte Carlo algorithmic to sample from this restricted space. These samples are then used to evaluate the impact of bilateral netting strategies to individual defaults and contagion. As an application, we employ this method to derivative networks and derive individual probabilities of default of banks. The comparison against popular alternative methods underlines the importance of restricting sample solutions to those compatible with the netting strategies of banks. We also provide an R package implementing our methodology.

A Preference-Based Evolutionary Biobjective Approach for Learning Large-Scale Fuzzy Cognitive Maps: An Application to Gene Regulatory Network Reconstruction

Learning large-scale fuzzy cognitive maps (FCMs) with the sparse attribute automatically from time series without prior knowledge remains a challenging problem. Most existing automated learning methods were applied to learn small-scale FCMs, and the learned FCMs are much denser than the maps constructed by human experts. Learning FCMs is the procedure of judging whether there are connecting edges and determining the weights of connecting edges. Thus, we transform the problem of learning FCMs into a biobjective optimization problem with two objects of minimizing the measure error and the number of nonzero entries, respectively. To solve this optimization problem, a preference-based iterative thresholding evolutionary biobjective optimization algorithm for learning FCMs is proposed. The strategy focuses on the knee area of the Pareto front (PF) with preference on the solutions near the true sparsity. Moreover, an initialization operator based on random forest is proposed to increase the speed of convergence toward the PF. The experiments on large-scale synthetic data with varying sizes and densities and the application to the gene regulatory network reconstruction problem have been conducted to demonstrate that our proposal matches or exceeds the existing state-of-the-art FCM learning approaches in most cases in terms of four measures, namely, Data_Error , Out_of_Sample_Error , Model Error, and SS_Mean . The Data_Error obtained by the proposed method can achieve 3.07E-06 even when the number of nodes reaches 200. We also demonstrate the effectiveness of the proposed initialization operator and the preference-based strategy, which can result in a fast convergence speed and higher accuracy.

Island division and multi-objective network reconstruction considering power flow entropy

Modern power system can identify component faults, isolate faults and resume operation quickly. In view of the problem that the distribution of line load in distribution network is not reasonable and it is easy to fall into the self-organized critical state, this paper introduces power flow entropy as an evaluation index to measure the robustness of power network reconstruction. Based on the power supply capability and node load level of distributed power supply in the process of network reconstruction, a strategy of island division is proposed. Then, a mathematical model is set up to minimize power flow entropy, network loss and node voltage drop, and the problem of network reconstruction after fault is solved by the improved chaos theory and binary particle swarm optimization algorithm. Finally, an example of IEEE-33 node distribution system is given to verify the feasibility of the proposed strategy and the effectiveness of the algorithm.

Analyses and applications of optimization methods for complex network reconstruction

Inferring the topology of a network from observable dynamics is a key topic in the research of complex network. With the observation error considered, the topology inferring is formulated as a connectivity reconstruction problem that can be solved through optimization estimation. It is found that the different optimization methods should be selected to deal with the different degrees of noise, different scales of observable time series and such other situations when it comes to the problem of connectivity reconstruction, which has not been analyzed and discussed before yet. In this paper, four regression methods, namely least squares, ridge, lasso and elastic net, are used to solve the problem of network reconstruction in different situations. In particular, a further analysis is made of the effects of each regression method on the network reconstruction problem in detail. Through simulation of a variety of artificial and real networks, as it has turned out, the four regression methods are effective in respect to network reconstruction when certain conditions are respectively satisfied. Based on the experimental results, it is possible to reach some interesting conclusions that can guide our readers to know the internal mechanisms for network reconstruction and choose the appropriate regression method in accordance with the actual situation and existing knowledge.