Structured sparsity learning for large-scale fuzzy cognitive maps

Fuzzy cognitive map (FCM) as a kind of intelligent soft computing method, by combining the advantages of neural network and fuzzy logic, can be used to mine the causal relationships between concepts and make reasoning. However, how to effectively learn the large-scale FCMs is still an open problem. In this article, by means of structured sparsity learning, a robust learning method for large-scale FCMs based on iterative smoothing algorithm is proposed. Firstly, in terms of sparse signal reconstruction, the objective function of learning method is constructed by using elastic and total variation (TV) penalties, which can be conducive to capture the sparse structure information of FCM and improve the robustness of network reconstruction. Due to the non-smoothness of the TV penalty, Nesterov's smoothing technique is used to solve the non-smooth problem, thus transforming the problem into a convex optimization problem. Subsequently, in order to quickly solve the convex optimization, the algorithm based on proximal gradient descent is applied. In the experiment part, synthetic FCM models with different densities, sizes and noises are used to evaluate the proposed method, and the experimental results demonstrate the proposed method can make full use of the observations to learn the structural information of FCM. Moreover, the real-world data from the gene regulatory networks (GRNs) are further used to evaluate the effect of network reconstruction, and a higher reconstruction accuracy can be verified.