Abstract-Short-term traffic forecasting based on deep learning methods, especially long short-term memory (LSTM) neural networks, has received much attention in recent years. However, the potential of deep learning methods in traffic forecasting has not yet fully been exploited in terms of the depth of the model architecture, the spatial scale of the prediction area, and the predictive power of spatial-temporal data. In this paper, a deep stacked bidirectional and unidirectional LSTM (SBU-LSTM) neural network architecture is proposed, which considers both forward and backward dependencies in time series data, to predict network-wide traffic speed. A bidirectional LSTM (BDLSM) layer is exploited to capture spatial features and bidirectional temporal dependencies from historical data. To the best of our knowledge, this is the first time that BDLSTMs have been applied as building blocks for a deep architecture model to measure the backward dependency of traffic data for prediction. The proposed model can handle missing values in input data by using a masking mechanism. Further, this scalable model can predict traffic speed for both freeway and complex urban traffic networks. Comparisons with other classical and state-of-the-art models indicate that the proposed SBU-LSTM neural network achieves superior prediction performance for the whole traffic network in both accuracy and robustness. Index Terms-Deep learning, bidirectional LSTM, backward dependency, traffic prediction, network-wide traffic HE performances of intelligent transportation systems (ITS) applications largely rely on the quality of traffic information. Recently, with the significant increases in both the total traffic volume and the data they generate, opportunities and challenges exist in transportation management and research in terms of how to efficiently and accurately understand and exploit the essential information underneath these massive datasets. Short-term traffic forecasting based on data driven models for ITS applications has been one of the biggest developing research areas in utilizing massive traffic data, and has great influence on the overall performance of a variety of In the last three decades, a large number of methods have been proposed for traffic forecasting in terms of predicting speed, volume, density and travel time. Studies in this area normally focus on the methodology components, aiming at developing different models to improve prediction accuracy, efficiency, or robustness. Previous literature indicates that the existing models can be roughly divided into two categories, i.e. classical statistical methods and computational intelligence (CI) approaches [2] . Most statistical methods for traffic forecasting were proposed at an earlier stage when traffic condition were less complex and transportation datasets were relatively small in size. Later on, with the rapid development in traffic sensing technologies and computational power, as well as traffic data volume, the majority of more recent work focuses on CI approaches for traffic forecasting. With the ability to deal with high dimensional data and the capability of capturing non-linear relationship, CI approaches tend to outperform the statistical methods, such as autoregressive integrated moving average (ARIMA) [36] , with respect to handling complex traffic forecasting problems [38] . However, the full potential of artificial intelligence was not exploited until the rise of neural networks (NN) based methods. Ever since the precursory study of utilizing NN into the traffic prediction problem was proposed [39], many NN-based methods, like feed forward NN [41], fuzzy NN [40], recurrent NN (RNN) [42] , and hybrid NN [25] , are adopted for traffic forecasting problems. Recurrent Neural Networks (RNNs) model sequence data by maintaining a chain-like structure and internal memory with loops [4] and, due to the dynamic nature of transportation, are especially suitable to capture the temporal evolution of traffic status. However, the chain-like structure and the depth of the loops make RNNs difficult to train because of the vanishing or blowing up gradient problems during the backpropagating process. There have been a number of attempts to overcome the difficulty of training RNNs over the years. These difficulties were successfully addressed by the Long ShortTerm Memory networks (LSTMs) [3] , which is a type of RNN with gated structure to learn long-term dependencies of Ruimin Ke is with the
Researchers in REF proposed a deep stacked bidirectional and unibidirectional LSTM (SBU-LSTM) neural network, which considered both forward and backward dependencies.
Deep Bidirectional and Unidirectional LSTM Recurrent Neural Network for Network-wide Traffic Speed Prediction
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Mathematics Computer Science