Research On Time Series Forecasting Method Based On Fuzzy Cognitive Map

As a kind of fuzzy system,fuzzy cognitive maps(FCMs)have been successfully used in modeling and dynamic analysis of many actual complex systems because of the combination of the advantages of fuzzy logic and neural network.In recent years,applications of FCMs in time series prediction received more and more attention.By modeling the historical observation values of a system,FCMs can mine the influences and interaction relationships between variables in the system,and then use the influence relationships to predict and analyze the system.However,the existing univariate time series prediction algorithms based on FCMs are inefficient when dealing with large-scale time series.The reason is that most methods use population-based learning methods.Secondly,existing methods cannot effectively extract features from non-stationary time series,and some prediction methods that use high-order fuzzy cognitive maps only take into account the high-order dependence and do not consider the degree of influence of different moments,resulting in low prediction accuracy.On the other hand,the existing multivariate time series prediction methods based on FCMs directly model all input and output variables,and do not mine effective information from historical data to reduce the complexity of the problem,making the algorithm inefficient.Given these shortcomings,this paper focuses on the study of time series forecasting based on FCMs.The main contents of the paper are as follows:(1)An FCM learning method based on the multi-scale quantum harmonic oscillator algorithm is proposed,combined with transfer entropy for multivariate time series forecasting.The proposed method can handle both the situations that the input and output variables are the same or not.First,the transfer entropy between every two variables is calculated based on the historical data.For the situations that the input and output variables are the same,the transfer entropy matrix is used to initialize the solutions.Otherwise,it is used to select key variables.Then the multi-scale quantum harmonic oscillator algorithm is employed to learn the weight matrix of the FCM constructed with the chosen variables.With the learned weight matrix,the feature values of the output variables can be predicted.Finally,experiments are carried out on multiple datasets and the results are compared with existing algorithms to verify the effectiveness of the proposed method.(2)A univariate time series forecasting algorithm based on empirical mode decomposition and high-order fuzzy cognitive maps is proposed.First,empirical mode decomposition is used to decompose the univariate time series to obtain multiple sub-sequences with different time scale features,forming the conceptual nodes of the FCM.Then the high-order fuzzy cognitive map is used to model the time series.To efficiently and accurately learn the weight matrix of a high-order fuzzy cognitive map,a learning method based on Bayesian ridge regression is proposed,which can estimate the regular term coefficients while learning the weight matrix,avoiding the subjectivity of artificial settings.Finally,forecasting can be conducted based on the learned weight matrix and the transfer characteristics of the highorder fuzzy cognitive map.In the experimental part,a series of experiments are conducted on eight public datasets.The results show that the proposed algorithm has good robustness to hyperparameters,and the comparison with existing methods also shows that the proposed algorithm is effective in large-scale non-stationary time series.(3)A time series prediction algorithm based on empirical mode decomposition and selfattention fuzzy cognitive maps is proposed,which mainly solves the problem that high-order fuzzy cognitive maps do not consider the degree of influence of different moments when modeling high-order dependencies.First,empirical mode decomposition is used to decompose the univariate time series to construct the conceptual nodes of the FCM.Next,the self-attention fuzzy cognitive map is proposed.By introducing the self-attention mechanism into the FCM,the state similarity between different moments is calculated to apply different attention strengths to different moments in the high-order dependencies,which also reduces the number of parameters.Finally,the gradient-based optimization algorithm is used to learn the parameter matrix for prediction.Experiments and results on six real datasets show that the prediction performance of the proposed algorithm is better than the existing algorithms.