Pearson correlation coefficient-guided large-scale fuzzy cognitive maps learning algorithm

Fuzzy cognitive maps (FCMs) are interpretable soft computing methods. In recent years, various algorithms have been proposed for automatically learning FCMs. However, the density of the weight matrix used for learning is often significantly higher compared with real FCMs. Moreover, the process involving learning causal relationships from large-scale data lacks guidance based on knowledge, so it is necessary to proactively explore the relationships between concept nodes to guide the learning process for FCMs. Inspired by the expert knowledge guidance used in the traditional algorithms for learning FCMs, we propose employing Pearson correlation coefficients (PCC) to guide the learning of FCMs. The PCC is a statistical measure used to assess the strength of the linear relationship between two variables, and it provides information about the strength and direction of the relationship. Therefore, we propose a new algorithm for learning large-scale FCMs with PCC guidance called PCCG-FCM. The PCCG-FCM model has the following three terms. The first term is an adaptive loss function to enhance the robustness of the model. The second term employs the $l_1$-norm to promote the sparsity of the weight matrix. The third term is our proposed PCC-guided term, where we leverage the PCC between the dependent and independent variables in a linear equation system to guide the learning of FCMs. We conducted several tests using real and artificial data. In addition, gene regulatory networks were reconstructed with the PCCG-FCM algorithm. The results showed that the proposed approach performed well.