Learning Large-Scale Fuzzy Cognitive Maps Based on Compressed Sensing and Application in Reconstructing Gene Regulatory Networks

Abstract

Learning large-scale sparse fuzzy cognitive maps (FCMs) from observed data automatically without any prior knowledge remains an outstanding problem. Most existing methods are slow and have difficulty in dealing with large-scale FCMs, because of the large searching space. We develop a framework based on compressed sensing (CS), a convex optimization method, to learn large-scale sparse FCMs, called CS-FCM. Combining with the sparsity of FCMs, the task of learning FCMs is first decomposed into sparse signal reconstruction problems. The ability of CS to exactly recover the sparse signals provides CS-FCM the probability to exactly learn FCMs. In the experiments, CS-FCM is applied to learn both synthetic data with varying sizes and densities and real-life data. The results show that CS-FCM obtains good performance by just learning from a small amount of data. CS-FCM can effectively learn sparse FCMs with 1000 nodes and even more, which have one million weights to be determined. CS-FCM is also applied to reconstruct gene regulatory networks (GRNs), and the well-known benchmark datasets DREAM3 and DREAM4 are tested. The results show that CS-FCM also obtains high accuracy in reconstructing GRNs. CS-FCM establishes a paradigm for learning large-scale sparse FCMs with high accuracy.