Ridge Regression And Generative Adversarial Network Based Learning Algorithms And Applications For Fuzzy Cognitive Maps

Inheriting the main properties of fuzzy logic and neural networks,fuzzy cognitive maps(FCMs)have found widespread applications.Constructed and learned from given time series,FCMs can serve as an inference algorithm to effectively model and mine the interrelationships between various entities in a complex system.The most popular FCM learning algorithms are evolutionary algorithms based,which can be used to learn FCMs with various sizes.However,existing evolutionary algorithms based FCM learning algorithms perform inefficiently when dealing with large-scale time series.Moreover,current FCM learning algorithms have to optimize each problem instance separately,since the learned model cannot be generalized to other new problem instances.To overcome these two limitations,this thesis focuses on proposing new FCM learning algorithms and exploiting FCMs for time series prediction and gene regulatory network reconstruction tasks.The main work can be summarized as follows,(1)An FCM learning algorithm based on ridge regression is proposed and applied to predict time series with the combination of redundant Haar wavelet transform.Current time series prediction models based on FCMs cannot be used to handle nonstationary large-scale time series,so our proposed time series prediction model first transforms univariate time series to multivariate time series using the redundant Haar wavelet transform;then the weight matrix parameter of FCMs is obtained by the proposed fast FCM learning algorithm based on ridge regression and finally the trained FCM model is used to forecast time series.The experimental results on eight benchmark datasets demonstrate the effectiveness of our proposal.The experimental results indicate the time series prediction model based on FCMs can be used to effectively solve the problem of nonstationary large-scale time series prediction.This algorithm is suitable for problem scenarios that focus on the accuracy of time series tasks rather than the reconstruction accuracy of graph structure space.(2)A FCM learning algorithm based on generative adversarial network is proposed.As the first deep graph generation model for transforming time series to graph structures,the proposed algorithm effectively addresses the problem of existing algorithms that the trained model cannot be directly used to solve new problem instances.The generator network in the algorithm first transforms multivariate time series into hidden state vector,which preserves the essential information in the original time series,and the resulting hidden state vector is constructed as the graph structure.The discriminator network in the algorithm first transforms both multivariate time series and FCM network to hidden vectors and calculates the similarity between these two hidden vectors as the similarity between multivariate time series and FCMs.The innovation of the proposed algorithm is that the trained model can be directly used to solve new problem instances without further optimization.Moreover,the discriminator network can be used to directly calculate the similarity between multivariate time series and FCMs,without the need of first transforming FCMs to multivariate time.Remarkable experimental results are obtained using the proposed FCM learning algorithm,which validates the effectiveness of the proposal.This algorithm is suitable for problem scenarios that focus on the accuracy of reconstruction of the spatial structure of the graph rather than the accuracy of the time series task.