Fast Learning Of Fuzzy Cognitive Map And Its Application In Data Classification

Fuzzy cognitive map is a directed graph model composed of concept nodes and weighted directed arcs connecting concept nodes.It combines the ideas of fuzzy logic and neural network,has powerful knowledge representation and reasoning capabilities,and is mainly used for complex modeling and analysis of dynamic systems.How to use historical data to automatically learn the weights of fuzzy cognitive maps is the focus of current fuzzy cognitive maps.At present,the weight learning of fuzzy cognitive maps based on historical data is usually divided into three categories: Hebbian-based learning methods,population-based learning methods,and hybrid learning methods.These learning methods have been applied to many fields and have shown good performance.However,these fuzzy cognitive map weight learning methods also have two obvious shortcomings:(1)The population-based learning method is difficult to deal with the learning problem of large-scale fuzzy cognitive map weights with hundreds or thousands of nodes.Moreover,the learning process is extremely time-consuming and computationally intensive;(2)These methods also do not take into account the influence of noise in the data on the learning of fuzzy cognitive map weights.Aiming at the shortcomings of existing learning methods,this paper proposes a fast learning method for fuzzy cognitive map weights.It first transforms the weight learning problem of fuzzy cognitive maps into a constrained least squares problem,and then By solving the least squares problem,the optimal weight matrix of the fuzzy cognitive map is obtained.Through a series of numerical experiments on artificial synthetic data sets,artificial synthetic data sets containing noise and public data sets,it is shown that the method proposed in this paper can quickly and effectively learn fuzzy cognitive maps of different scales,and can handle noise-containing data learning problem of fuzzy cognitive map weights.Furthermore,according to the structural characteristics and inference rules of fuzzy cognitive maps,this paper proposes two classifiers based on fuzzy cognitive maps.First,the attributes and categories in the classification data set are respectively mapped to attribute nodes and class nodes in the fuzzy cognitive map.Then,the two proposed fuzzy cognitive map classifiers are learned through the fast learning method proposed in this paper.Finally,use the reasoning ability of the fuzzy cognitive map to predict the sample category.Experimental results on artificial synthetic data sets and 5 public data sets show that the two fuzzy cognitive map classifiers proposed in this paper have good classification results.