A Capsule Network for Traffic Speed Prediction in Complex Road Networks

Abstract

This paper proposes a deep learning approach for traffic flow prediction in complex road networks. Traffic flow data from induction loop sensors are essentially a time series, which is also spatially related to traffic in different road segments. The spatio-temporal traffic data can be converted into an image where the traffic data are expressed in a 3D space with respect to space and time axes. Although convolutional neural networks (CNNs) have been showing surprising performance in understanding images, they have a major drawback. In the max pooling operation, CNNs are losing important information by locally taking the highest activation values. The inter-relationship in traffic data measured by sparsely located sensors in different time intervals should not be neglected in order to obtain accurate predictions. Thus, we propose a neural network with capsules that replaces max pooling by dynamic routing. This is the first approach that employs the capsule network on a time series forecasting problem, to our best knowledge. Moreover, an experiment on real traffic speed data measured in the Santander city of Spain demonstrates the proposed method outperforms the state-of-the-art method based on a CNN by 13.1% in terms of root mean squared error.Index Terms-traffic speed prediction, capsule network (Cap-sNet), convolutional neural network (CNN)

Structural Recurrent Neural Network for Traffic Speed Prediction

“…The mean relative er- ror (MRE) is one of the most common metrics to quantify the accuracy of different prediction models in general. However, the error of a larger value of speed might result in a smaller MRE and vice versa, providing inconsistent results as witnessed in [6]. Thus, we employ mean absolute error (MAE) and root mean squared error (RMSE) as more intuitive metrics for assessing the speed prediction performance.…”

“…Meanwhile, the number of trainable parameters of the SRNN is 1.1 × 10 6 , which is independent of the sequence length l. In fact, the size of the trainable parameter set of the SRNN is affected only by the size of the RNNs. The image-based approaches [5,6] would face a significant increase in the computation time as the sequence length l and the number of road segments N increase. On the other hand, the SRNN is scalable to varying l and N , and can learn the spatio-temporal traffic characteristic with much fewer parameters given the topological information.…”

“…The deep neural network captures the spatio-temporal characteristics by learning the images. Recently, a capsule network (CapsNet) architecture proposed in [6] has been demonstrated to outperform the state-of-the-art in complex road networks. The dynamic routing algorithm of the CapsNet replaces the max pooling operation of the CNN, resulting in more accurate predictions but more parameters to train.…”

SBAG: A Hybrid Deep Learning Model for Large Scale Traffic Speed Prediction

“…To make progress in the accuracy of traffic prediction, hybrid models are used in traffic speed prediction. In complex road network CapsNet [13] architecture proposed which replaced the max polling operation of CNN. To cope with the temporal evolution of traffic status, Recurrent Neural Networks (RNNs) models are specifically very appropriate because of the dynamic nature of transportation.…”

Zero-skipping in CapsNet. Is it worth it?

“…Capsule Network (CapsNet) is the next-generation neural network and has drawn the attention of researchers in the past few years [7]- [10]. The concept "Capsule" was first introduced in [11] but there was no practical implementation until Sabour et al introduced "Dynamic routing between Capsules" [12] and presented a practical new network based on capsules called Capsule Network.…”