Learning sparse Fuzzy Cognitive Maps by Ant Colony Optimization

Abstract

Fuzzy Cognitive Maps (FCMs) are a causal modelling technique. FCM models contain nodes (representing the concepts to be modelled) and directed weighted edges (representing the causal relations between the concepts). Data-driven FCM learning algorithms are an objective approach with the potential to discover the causal relations that are unknown to human experts. Learning FCM from data can be a difficult problem because the size of the solution space grows quadratically with the number of nodes in the FCM models. A data-driven learning algorithm based on Ant Colony Optimization (ACO) is proposed to develop Fuzzy Cognitive Maps (FCMs). The FCM models can be isomorphically represented as weight vectors. The objective function is to minimize the difference between the estimated response of the FCM model and the target response observed from the to-be-modelled system. An ACO algorithm with heuristic information is proposed to find the best FCM model. The performance of the ACO algorithm was tested on both randomly generated data and DREAM4 project data (publicly available in-silico gene expression data). The experiment results show that the ACO algorithm is able to learn FCMs with at least 40 nodes.