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• A novel GCN model is proposed for multivariate time series prediction. • EMD is used to extract multi-scale temporal features of original time series. • Multi-head attention mechanism is utilized to explore the spatial dependencies. • Real datasets from various fields confirms the superiority of the method. Modeling for multivariate time series have always been a meaningful subject. Multivariate time series forecasting is a fundamental problem attracting many researchers in various fields. However, most of the existing methods focused on univariate prediction and rarely take into account the potential spatial dependencies between multiple variables. Multivariate time series forecasting can be naturally viewed from graph perspective, where each variable from multivariate time series can be viewed as a node in the graph, and they are interlinked through hidden dependencies. Therefore, a novel graph neural network model based on multi-scale temporal feature extraction and attention mechanism is proposed for multivariate time series prediction. Specifically, empirical modal decomposition is used to extract the time-domain features of multivariate time series at different time scales to form the node features of the graph. Meanwhile, the multi-head attention mechanism is applied to construct potential associations between nodes and enhance the rationality of relationships in the graph. Furthermore, the graph convolutional neural network is used to generate node embeddings that contain rich spatial relationships. Finally, the temporal convolutional network establishes temporal relationships for the node embedding to achieve multivariate time series prediction. The real data from the financial, traffic and medical fields confirm the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

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. • A robust learning method for large-scale FCMs with structured sparsity. • Three regularizations are introduced to improve robustness against insufficient data and high noise. • An efficient algorithm with the Nesterov's smoothing technique is utilized. [ABSTRACT FROM AUTHOR]