Deep attention fuzzy cognitive maps for interpretable multivariate time series prediction

Although time series prediction is widely used to estimate the future state of complex systems in various industries, accurate, interpretable and generalizable methods are still limited when used to make long-term nonstationary predictions. To this end, this article proposes deep attention fuzzy cognitive maps (DAFCM), which is composed of spatiotemporal fuzzy cognitive maps (STFCM), long short-term memory (LSTM) neural network, temporal fuzzy cognitive maps (TFCM) and residual structures. First, an improved attention mechanism is used to build spatiotemporal fuzzy cognitive maps that capture the spatial correlation in pairs of nodes and the temporal correlation of respective nodes. Second, the node state updated through the STFCM is input to the LSTM to capture the long-term trend of these series, and the TFCM with improved time attention is applied for the nonstationary problem in the time series. Finally, we add the state values of previous nodes into the DAFCM and build residual structures through linear transformation to prevent gradient explosion and gradient disappearance in long-term backpropagation. By combining the interpretability of fuzzy cognitive maps (FCM) and the high prediction accuracy of deep learning, the DAFCM can be used to accomplish tasks such as multivariate long-term nonstationary time series forecasting in multiple domains, and its efficiency is validated with 6 public datasets across 9 baselines.