Complex Network Reconstruction Based On Time Series Data

In real life,complex systems can be seen in everywhere.They are closely related to people’s life,and exist in many fields such as social,economic,physical,biological,ecological and so on.In order to facilitate the research of complex systems,complex networks are always seen as the abstract description of complex systems where a single node in a network corresponds to a single individual in the system,and the edges between nodes in the network correspond to the individual Interrelationships.Therefore,the study of complex networks plays a very important role in understanding the topology and various dynamic behaviors of complex systems.How to understand the interaction between individuals in complex systems and to predict and control complex system behavior by studying complex networks has become the focus of attention of various disciplines.However,many of the complex network topologies are partly even totally unknown,they can not be directly detected or the detection cost is huge,such as gene regulation network,social network,brain function network.Therefore,according to the detectable data to indirectly infer and reconstruct the network topology has important research significance and scientific value.This paper studies the reconstruction of complex network based on time series data.The main contents of this paper are as follows: 1.Network reconstruction based on one-dimensional dynamics equations and time series data.In this paper,we study the problem of network reconstruction based on time series data and one-dimensional dynamical equations.We use a decomposition model to reconstruct the network.Each node is reconstructed separately,we only reconstruct the edges which are pointing to the same node at a time.In this paper,an algorithm based on stochastic gradient descent method is proposed to reconstruct the network by time series data.The time series data are divided into many small samples,and the adaptive learning rate is proposed.Combined with the stochastic gradient descent method,the performance is good enough.Experiments show that the results of reconstruction by our algorithm are excellent in both the model error and the AUC performance measures,and the high efficiency of the proposed algorithm shows the potential of reconstructing the large-scale network.2.Network reconstruction based on multidimensional dynamical equations and time series data.In this paper,we also studied the problem of network reconstruction based on multidimensional dynamical equations.The multidimensional dynamical equations are several differential equations.This paper reconstructs the network according to the time series data generated by the differential equation.We combine a common network model with a chaotic system and use python’s differential function to obtain time series data.Then,three objective functions are proposed for the multidimensional dynamical equation.Combining with the stochastic gradient descent method,the optimization of the objective function is also carried out randomly.Finally,the network is reconstructed according to the three updating formulas.The experimental results show that the algorithm is good at reconstructing the network based on the time series data which is generated by the multidimensional dynamical differential equation.3.Network reconstruction based on time series data with noises.In this paper,we study the network reconstruction based on the time series data with noise.In this paper,we study the network reconstruction problem of time series data of Gaussian white noise with different intensities.In this paper,two algorithms are proposed for experiment,which are stochastic gradient descent based algorithm and least squares method based algorithm.The two algorithms are experimented on all the data sets,and the model errors of the experimental results are analysed.Then the advantages and disadvantages of the two algorithms are analysed.In this paper,it is found that the algorithm can be reconstructed using the least squares method based algorithm when the amount of data is small,and when the amount of data is relatively large,the algorithm can be reconstructed by the stochastic gradient descent based algorithm.In addition.If you need to continue to add data for online learning,the stochastic gradient descent based algorithm is a better choice.