Identifying network topologies is a matter of great concern for us to better understand the evolutionary mechanisms and grasp the collective dynamics of complex networked systems. In this paper, a unified methodological framework for reconstructing nonlinear networks is proposed, termed Group Sparse Penalized Nonlinear Least Squares. Based on the theory of function approximation and feature selection, a nonlinear framework is firstly formulated with the equation of polynomial combination, where polynomial basis functions corresponding to the specific node should be taken as a group for either elimination or selection. Then the topology of complex networked system would be identified by solving the problem of sparse group optimization. Finally, the performance of our proposed method is evaluated on synthetic datasets from the classical Kuramoto oscillator model. Different influential cases of topology identification are also considered. All of the results demonstrate that the high-precision and robustness of our proposed method.
When inferring the undergoing network structure, which describes the dynamic mutual influence among large scale variables, it is a challenge to take full advantage of structural prior information when it is available. In this paper, we focus on reconstruction of piecewise-constant time-varying small-world networks. Specifically, we propose an identification method incorporating structural properties as prior information, including the average degree of the network. On the one hand, we adjust the network sparsity by re-weighting l1 norm according to the deviation of the estimated average degree, based on the assumption that the average degree is almost constant over time. On the other hand, for each node in the network, we encourage the existence of potential associated edges while discouraging non-existing edges based on predictions from the previous iteration. Finally, an adaptive LASSO algorithm is utilized to uncover the time-varying structures which performs better on small-world networks when comparing with the method without prior information.
Recently, constructing relatively accurate gene regulatory networks has become a hot research direction in the field of bioinformatics. Path consistency algorithm based on conditional mutual information (PCACMI) is a practical algorithm to reconstruct gene regulation networks, but the threshold is fixed, which will affect the accuracy of the reconstructed networks. So we improve PCACMI and design a new algorithm termed dynamic threshold condition mutual information (DTCMI). In the new algorithm, the threshold is related to the maximal element of the weight matrix of different orders, and the value of threshold will change with maximal weights. In addition, in order to improve the accuracy of the reconstructed network, we firstly employ resampling strategy by utilizing the jackknife to deal with the gene expression data. Finally, we reconstruct the networks by using gene knock-out expression data from the stochastic differential equation and DREAM4 challenges. The results show that the performance of DTCMI is more effective.
Utilizing gene expression data to infer gene regulatory networks has received great attention because gene regulation networks can reveal complex life phenomena by studying the interaction mechanism among nodes. However, the reconstruction of large-scale gene regulatory networks is often not ideal due to the curse of dimensionality and the impact of external noise. In order to solve this problem, we introduce a novel algorithms called ensemble path consistency algorithm based on conditional mutual information (EPCACMI), whose threshold of mutual information is dynamically self-adjusted. We first use principal component analysis to decompose a large-scale network into several subnetworks. Then, according to the absolute value of coefficient of each principal component, we could remove a large number of unrelated nodes in every subnetwork and infer the relationships among these selected nodes. Finally, all inferred subnetworks are integrated to form the structure of the complete network. Rather than inferring the whole network directly, the influence of a mass of redundant noise could be weakened. Compared with other related algorithms like MRNET, ARACNE, PCAPMI and PCACMI, the results show that EPCACMI is more effective and more robust when inferring gene regulatory networks with more nodes.
To improve the decoupling control ability and robustness of nonlinear high coupling two-motor variable frequency speed-regulating systems(TVFSS),the two-degree-of-freedom internal model control(2-DOF IMC)is proposed based on neural network generalized inverse(NNGI).On the basis of reversibility analysis of the original system,the generalized inverse model approximated by the dynamical neural network is cascaded with the original system.Based on the idea of NNGI,the decoupling linearization and open-loop stability of system are reached.The robust stability is improved by introducing 2-DOF IMC to generalized pseudo-linear system.The results of experimental researches based on ST-300 PLC show that the decoupling control of the system can be realized successfully and the high control performance can be ensured when the system has inverse modeling errors and changeable load.
For complex networked systems, based on the consideration of nonlinearity and causality, a novel general method of nonlinear causal network learning, termed extreme support vector regression Granger causality (ESVRGC), is proposed. The nonuniform time-delayed influence of the driving nodes on the target node is particularly considered. Then, the restricted model and the unrestricted model of Granger causality are, respectively, formulated based on extreme support vector regression, which uses the selected time-delayed components of system variables as the inputs of kernel functions. The nonlinear conditional Granger causality index is finally calculated to confirm the strength of a causal interaction. Generally, based on the simulation of a nonlinear vector autoregressive model and nonlinear discrete time-delayed dynamic systems, ESVRGC demonstrates better performance than other popular methods. Also, the validity and robustness of ESVRGC are also verified by the different cases of network types, sample sizes, noise intensities, and coupling strengths. Finally, the superiority of ESVRGC is successful verified by the experimental study on real benchmark datasets.
Network topology represents the influencing mechanism of complex networked system. So it is very important to infer network topology based on the measured data in various fields. In this paper, based on the consideration of nonlinearity, causality and sparsity, a novel method is proposed, termed Block Orthogonal Matching Pursuit-Nonlinear Conditional Granger Causality (BOMP-NCGC). Firstly, Gaussian kernel function is used for fitting the nonlinear system model and the formulation of nonlinear conditional Granger causality is illustrated. Secondly, the block orthogonal matching pursuit is adopted for group sparse selection. Finally, based on the construction of restricted and unrestricted model, nonlinear conditional Granger causality is applied for causal judgement to get the network topology. As a result, the verification of performance is executed by the classical model of gene regulatory network. Compared with linear conditional Granger causality and nonlinear conditional Granger causality, BOMP-NCGC demonstrates the superiority and robustness across the different types of networks.
Reconstructing time-delayed interactions among nodes of nonlinear networked systems based on time-series data is important and challenging, especially for the cases with only limited noisy data but no knowledge of node dynamics. In this paper, by fusing multiple source datasets together, we propose a data-driven modeling method based on noisy time series, referred to as nonuniform embedding nonlinear conditional Granger causality (NENCGC), specially focusing on the nonlinearity and nonuniform time-delayed characteristics of real networked systems. Specifically, we first use a nonuniform embedding scheme to select causal lagged components and then group these selected lagged components into different clusters of different nodes. In nonlinear causal analysis, the lagged components in the same cluster are treated as a whole through radial basis functions to fit the nonlinear relationships among nodes. Compared with other popular methods, our proposed NENCGC is proved effective and accurate in discovering time-delayed interactions from noisy data in terms of standard metrics. Meanwhile, both superiority and robustness of NENCGC against the variations of samples, time delays, noise intensities, as well as coupling strengths, are demonstrated.
In order to improve the robustness and anti-interference ability of induction motor variable frequency speed control system (IMVFSCS), a modified internal model control (MIMC) method based on neural network generalized inverse (NNGI) was proposed. On the basis of reversibility analysis of original system, the generalized inverse model approximated by the dynamical BP neural network was cascaded with the original system. Based on the idea of NNGI, linearization and open-loop stability of system can be reached, which benefits the integration of control system. Then the robust stability can be improved by introducing modified internal model control method to generalized pseudo-linear system. The results of experimental researches demonstrate that the linearization of the system can be realized successfully and the high performance of speed control can be ensured when the system has inverse modeling errors and changeable load.
'/%3e%3cuse xlink:href='%23a' transform='rotate(23.036 .093 25.536)'/%3e%3cuse xlink:href='%23a' transform='rotate(45.87 1.273 16.18)'/%3e%3cuse xlink:href='%23a' transform='rotate(69.945 .996 12.078)'/%3e%3cuse xlink:href='%23a' transform='rotate(20.66 -19.689 31.932)'/%3e%3c/svg%3e)