Research On Sparse Fuzzy Cognitive Map Learning Methods Based On Evolutionary Algorithms

In recent years,due to the simple form,good interpretability,and fast reasoning ability,fuzzy cognitive maps(FCMs)have attracted wide attention of the academe,and have been fully applied in real life.In order to extend FCMs to more fields,learning high-precision FCMs has become a core research task.The high-precision FCMs have two main characteristics: first,FCMs should have strong numerical fitting ability to the time series;second,we hope that FCMs not only have a good numerical fitting ability,but their model structures should be also more suitable for the real model.An important feature of FCMs in reality is that they are often sparse.At present,many effective algorithms focus on improving the numerical fitting ability of the model as much as possible,and often ignore the sparse structure that the real model should have.In addition,the current data often contains noise.In order to make the learned FCMs closer to reality,we also hope that FCMs have the ability to resist noise as much as possible.This thesis mainly studies how to design FCM learning algorithms,so that the algorithms can obtain the model with sparse structure while improving the numerical fitting ability.The main work is summarized as follows:Sparse fireworks algorithm for FCM learning: At present,most of the evolutionary algorithms for learning FCMs are not concise and fast enough,while fireworks algorithm should be considered as a new fast and simple evolutionary algorithm.It has been applied in non-negative matrix decomposition,image recognition and filter design.However,the sparse fireworks algorithm has neither been used to learn FCMs nor can learn sparse models.Therefore,a sparse fireworks algorithm for learning sparse FCMs(SFWA-FCM)is proposed.SFWA-FCM applies a new mutation explosion operator to learn sparse structures.The experimental results on synthetic and real data of SFWA-FCM show better modeling ability and numerical fitting ability.Compared with the existing algorithms,SFWA-FCM shows high efficiency and accuracy.Density-controlled Memetic algorithm for FCM learning: At present,most sparse FCM learning algorithms use mutation operation to control the density of models,while mutation operation is mainly used to expand population diversity,and frequently using mutations may cause the instability of the algorithm.To this end,a density-controlled memetic algorithm(DC-MA)is designed.DC-MA uses the crossover operator for controlling density,which better fulfills our expectations.At the same time,a lot of experiments is conducted on synthetic and real-life data.The results show that the numerical fitting ability of DC-MA is better than that of most sparse learning algorithms,and the modeling ability and numerical fitting ability are better than those of traditional evolutionary algorithms.The stability of the algorithm has also been improved significantly.Two-stage transfer entropy Memetic algorithm for FCM learning: With the application of sparse learning algorithms on FCMs,we need more fast and accurate algorithms.Currently sparse FCM learning algorithms can be divided into two categories.One is one-stage algorithms for learning weights and controlling density at the same time.They have the following problems: Sparse and optimized operations are used while learning,so that the algorithms have a huge search space.Existing algorithms often fail to meet the requirements in time.The other pre-analyzes the time series to obtain the initial model,and then to optimize using the two-stage learning algorithm.This kind of algorithm often does not follow the causality of FCM model when determining the initial structure,thus destroying the interpretability of FCMs.In addition,real-world data is usually noisy.To this end,we propose a two-stage memetic learning algorithm based on transfer entropy(TE-FCM).TE-FCM firstly obtains the initial structure of the model by passing the entropy,and the transfer entropy guarantees the causality of the model to a certain extent.Secondly,the improved memetic algorithm can correct the initial structure to some extent.Finally,the Huber loss is used as the evaluation function.The capability of the algorithm against noise is also improved which plays an important role in real world data with noises.