Deep belief improved bidirectional LSTM for multivariate time series forecasting

Multivariate time series (MTS) play essential roles in daily life because most real-world time series datasets are multivariate and rich in time-dependent information. Traditional forecasting methods for MTS are time-consuming and filled with complicated limitations. One efficient method being explored within the dynamical systems is the extended short-term memory networks (LSTMs). However, existing MTS models only partially use the hidden spatial relationship as effectively as LSTMs. Shallow LSTMs are inadequate in extracting features from high-dimensional MTS; however, the multilayer bidirectional LSTM (BiLSTM) can learn more MTS features in both directions. This study tries to generate a novel and improved BiLSTM network (DBI-BiLSTM) based on a deep belief network (DBN), bidirectional propagation technique, and a chained structure. The deep structures are constructed by a DBN layer and multiple stacked BiLSTM layers, which increase the feature representation of DBI-BiLSTM and allow for the model to further learn the extended features in two directions. First, the input is processed by DBN to obtain comprehensive features. Then, the known features, divided into clusters based on a global sensitivity analysis method, are used as the inputs of every BiLSTM layer. Meanwhile, the previous outputs of the shallow layer are combined with the clustered features to reconstitute new input signals for the next deep layer. Four experimental real-world time series datasets illustrate our one-step-ahead prediction performance. The simulating results confirm that the DBI-BiLSTM not only outperforms the traditional shallow artificial neural networks (ANNs), deep LSTMs, and some recently improved LSTMs, but also learns more features of the MTS data. As compared with conventional LSTM, the percentage improvement of DBI-BiLSTM on the four MTS datasets is 85.41, 75.47, 61.66 and 30.72%, respectively.