Sparse and regression learning of large-scale fuzzy cognitive maps based on adaptive loss function

Fuzzy cognitive maps (FCMs) learning is a hot topic in recent years. However, as the number of concepts increases in FCMs, it is difficult to learn the sparse and robust FCMs from a small amount of data, especially from noise data. In this paper, a new large-scale FCMs learning method based on the sparse regression of adaptive loss function is presented, marked as AQP-FCM. Adaptive loss function and L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document}-norm are introduced in the model to deal with noise data. We solve the model by ADMM method and quadratic programming method to learn the FCMs better. Moreover, the convergence of model is proved. We did a series of experiments under the synthetic data of time series and noise synthesis data. AQP-FCM is also applied to reconstruct gene regulatory network (GRNs). The results of the experiments show that the proposed AQP-FCM method has good performance.