Complex System Reconstruction Algorithm Based On Time Series And Its Application

With the rise of big data and artificial intelligence,time series data has become an important monitoring data in the fields of finance,industry,medicine,etc.People can predict the future trend,monitor the abnormal situation or classify the recorded data through the known time series.In fact,many complex systems can not be observed directly,but the internal relations of complex systems can be reconstructed through time series,which is of great significance for the control of complex systems.Therefore,how to reconstruct complex systems from time series has become a hot issue and challenging problem.To accurately reconstruct complex systems from time series,it is necessary to have correct problem modeling,excellent optimization algorithm and pointed evaluation criteria.In this paper,the reconstruction of complex systems based on time series is modeled from a new perspective and advanced optimization algorithms are explored.Two typical complex systems,fuzzy cognitive map(FCM)and complex networks,are taken as the main research targets and the purpose of this paper is to model them with high accuracy from time series.Also,the proposed algorithm is used in a practical application case.In the aspect of problem modeling,by analyzing the characteristics of complex system reconstruction problem,the reconstruction problem is described as a multi-objective and multi-task optimization problem;in the aspect of optimization algorithm,by deeply studying the characteristics of the problem,the optimization algorithm with preference and the optimization algorithm based on sparse operator are designed.To verify the key role of complex system reconstruction in practical application,this paper also applies it to the actual case of Electroencephalogram(EEG)signal forecasting.The main works of this paper are summaried as follows:1.It is still a challenging problem to automatically learn large-scale FCMs with sparse attributes from time series.Most of the existing automatic learning methods are used to learn small-scale FCMs,and the density of the learned FCM is much denser than the map constructed by human experts.In order to construct an FCM closer to the real density,we define the problem as a two-objective optimization problem.In addition to minimizing the measure error,sparsity is also regarded as another optimization objective.In order to solve this problem,we propose a preference-based iterative thresholding learning strategy,which focuses on searching the knee area of Pareto front.In addition,an initialization operator based on random forest is proposed to improve the convergence speed.Experiments on FCMs with different sizes and densities show that the proposal can significantly improve the learning accuracy compared with state-of-the-art methods.It is also proved that the initialization operator and the strategy with preference can lead to faster convergence speed and higher accuracy.2.Due to the diversity of complex systems,in practical applications,it is common to learn two or more FCMs at the same time,and these FCMs may share similar patterns.However,existing FCM learning algorithms can only learn a single FCM,which makes the share of the similar patterns between them impossible.Meanwhile it is inefficient.Considering these problems,we model the multiple FCM learning problem as a multi-task optimization problem.Each FCM learning problem is taken as a task under the framework of the evolutionary multi-task optimization,and each of them is a multi-objective optimization problem.In order to learn large-scale FCMs,we use the decomposition strategy to decompose high-dimensional optimization into small-scale subproblems.Besides,we design a local search operator based on the iterative thresholding method.Experiments are conducted on the double FCM learning problem with different number of nodes,densities and activation functions.The results show that the model can learn similar FCMs simultaneously with faster convergence speed and smaller data error compared with single task optimization.3.In recent years,FCM has been successfully applied to time series forecasting.However,it is still a challenge to predict long non-stationary multivariate time series such as EEG signals.We propose an efficient time series prediction model based on elastic net and highorder FCM,which not only considers the interaction between variables,but also captures long time dependency.Human action prediction through EEG signal is taken as a case study to verify the effectiveness of the algorithm in forecasting long non-stationay multivariate time series.Specifically,we first predict EEG signals,then use one-dimensional convolution neural network(1d-CNN)to classify the predicted time series,so as to obtain the specific human action.Experimental results on the Grasp-and-Lift dataset show that the proposal can obtain the lowest prediction error in most cases compared with other regression methods.And the classification performance of 1d-CNN is better than that of the latest EEG data classification methods.The results show that the proposed method can predict and classify long non-stationary multivariable time series with high accuracy and efficiency.4.The complex network is another important form of the complex system.Reconstructing the structure of complex networks from time series is a significant but challenging problem.In real-world applications,it is often necessary to reconstruct two or more complex networks at the same time.However,the existing network reconstruction algorithms can only deal with one problem at a time,which do not consider the correlation between similar networks.In order to explore similar network structure patterns among different tasks,this paper establishes an evolutionary multitasking framework to optimize multiple network reconstruction tasks at the same time.Each task is modeled as a single objective function including both reconstruction error and structure error.The online learning method is used to learn the parameter controlling the amount of genetic material exchange,which avoids the negative transfer between tasks and allows the transfer of useful information between tasks.Experiments on three dynamic models,synthetic and real-world networks show that the model is superior to state-of-the-art methods in terms of all evaluation criteria.5.Complex networks are sparse in nature.However,existing network reconstruction algorithms based on evolutionary optimization do not consider how to deal with sparse solutions with mostly zero decision variables.Hence,we propose the sparse multi-agent genetic algorithm to better find the sparse optimal solution.Sparse genetic operators are designed to ensure the sparsity of the solution during the iteration.Experiments on three network dynamics and six real-world networks with different scales show that the algorithm can search the sparse optimal solution effectively,and the self-learning operator can significantly improve the network reconstruction performance.