Robust learning of large-scale fuzzy cognitive maps via the lasso from noisy time series

Fuzzy cognitive maps (FCMs) have been used to describe and model the behavior of complex systems. Learning large-scale FCMs from a small amount of data without any a priori knowledge remains an outstanding problem. In particular, a significant challenge arises when limited amounts of data are accompanied by noise. Here, we develop a framework based on the least absolute shrinkage and selection operator (lasso), a convex optimization method, to robustly learn FCMs from noisy data, which is termed LASSOFCM. In LASSOFCM, the task of learning FCMs is decomposed into sparse signal reconstruction problems owing to the sparseness of FCMs. In the experiments, LASSOFCM is applied to learn synthetic data with varying sizes and densities. The results show that LASSOFCM obtains good performance in learning FCMs from time series with or without noise and outperforms the existing methods. Moreover, we apply LASSOFCM to reconstruct gene regulatory networks (GRNs) using the benchmark dataset DREAM3 and DREAM4, and LASSOFCM achieves good performance. LASSOFCM establishes a paradigm for learning large-scale FCMs with high accuracy and has potential applications in a wide range of fields.