Learning Fuzzy Cognitive Maps from Data by Ant Colony Optimization

Fuzzy Cognitive Maps (FCMs) are a flexible modeling technique with the goal of modeling causal relationships. Traditionally FCMs are developed by experts. We need to learn FCMs directly from data when expert knowledge is not available. The FCM learning problem can be described as the minimization of the difference between the desired response of the system and the estimated response of the learned FCM model. Learning FCMs from data can be a difficult task because of the large number of candidate FCMs. A FCM learning algorithm based on Ant Colony Optimization (ACO) is presented in order to learn FCM models from multiple observed response sequences. Experiments on simulated data suggest that the proposed ACO based FCM learning algorithm is capable of learning FCM with at least 40 nodes. The performance of the algorithm was tested on both single response sequence and multiple response sequences. The test results are compared to several algorithms, such as genetic algorithms and nonlinear Hebbian learning rule based algorithms. The performance of the ACO algorithm is better than these algorithms in several different experiment scenarios in terms of model errors, sensitivities and specificities. The effect of number of response sequences and number of nodes is discussed.